Blood on the Ice

Background
Blood on the Ice is a multi-step quest initiated in Windhelm. It entails discovering the identity of a serial killer that has killed at least 3 young women by the time Windhelm is entered by the player. The body of the latest victim is in the cemetery, and the quest is activated when the nearby Windhelm guard is queried. There are alternative paths through the quest, so following the quest markers exactly may not be optimum. There isn't really any forensic reasoning involved, although there is a nod to CSI; common sense will suffice for the initial portion. The warning about alternate routes through the quest should alert the player to question some early conclusions the various dialog options seem to force. The walkthough below gives the details.

Walkthrough
At this point, the player can complete this quest in one of two ways:
 * 1) Enter into Windhelm 4 times. Upon the 4th, head to the Graveyard around 2 AM. If you are in the middle of or have finished The Dark Brotherhood questline, this could hinder your possibilities of getting this Quest.
 * 2) Approach the graveyard outside the Hall of the Dead at night; there will be several people gathered around a female corpse.
 * 3) Speak with the guard.
 * 4) Question three witnesses.
 * 5) Visit Jorleif to be granted permission to help the investigation.
 * 6) Return to the guard.
 * 7) Enter the Hall of the Dead and speak with Helgird.
 * 8) Return to the body, follow the trail of blood to Hjerim.
 * 9) Return to Jorleif for advice.
 * 10) Pick the lock or receive a key from the Tova Shatter-Shield, Friga Shatter-Shield's mother and enter the house.
 * 11) Investigate all of the furniture that gives you the option. The wardrobe on the right in the northwest room of the house will have a hidden door leading to an altar and take Butcher Journal from the altar.
 * 12) Take the Butcher's Journal #1, exit and grab the first journal from the bloody chest up against the wall, Strange Amulet and flier from the shelf (if you turn around and face the main door, the amulet is on the shelves on the right side of the door, under the fliers).
 * 13) You have to visit Jorleif before visiting the Candlehearth Hall or Calixto's House of Curiosities to speak with Calixto Corrium. You can show him the Strange Amulet and even sell it to him, if you so choose. He will tell you it belongs to the court mage. Note that you need the amulet in order to accuse the mage, however.
 * 14) Visit Viola Giordano. She's often found in Candlehearth Hall (note: you can't talk to her if you don't have a copy of the "Beware the Butcher" pamphlet in your inventory or if she is dead or missing). Note also that if you pick up the journal before talking to her in the house, you can drop the journal and pick it up in front of her to continue the accusation quest line.

Accuse the mage

 * 1) Return to Jorlief to end the quest and thus accuse the court mage of the murders.

Catch the killer
Note: If you sold the amulet to Calixto earlier, after you "catch" (kill) the murderer, you can loot the complete amulet (Necromancer Amulet) off the body. It grants +50 Magicka, Fortify Conjuration 25%, and reduces Health and Stamina regeneration by 75%.
 * 1) Go and talk to Wuunferth the Unliving, the court mage, rather than following the quest marker to Jorleif. Tell him you heard he was practicing necromancy. He tells you he doesn't, and that the amulet and journals are not his.
 * 2) Go to the marketplace area (right by the White Phial shop; the map indicator will be a little misleading) in the stone quarter at night, as Wuunferth suggests, find and stop Calixto, who is about to strike again.
 * 3) Alternatively, instead of stopping Calixto in the marketplace, if you witness him successfully carrying out this murder, he will run off into the night. Your quest tracker will then lead you back to Hjerim, where the killer lies in wait and will attack you immediately upon entering. Alternatively, if the player is fast enough, they can catch up to Calixto and strike him down, with no added bounty.
 * 4) Return to Jorleif and tell him that the killer has been caught.

Bugs

 * Sometimes, after accusing Wuunferth, the body will not appear outside Candlehearth Hall. This can be remedied by talking to Wunnferth (who is out of jail) and triggering the next phase of the quest.
 * Sometimes after you complete the entire quest and you buy all of the upgrades for your house, when you go inside the alchemy lab/arcane enchanter room, the altar and all the bones will still be there and you will not be able to use any weapon racks or display cases in the house.
 * If you begin this quest, take over Windhelm, and then try to complete it afterwards, you may notice that the crime scene is no longer there, though you may still have an objective to investigate it, depending on how far into the quest you were when you took over the city. For example, if you have finished the quest and Windhelm is still destroyed, and you go to see Calixto strike Elda Early-Dawn in the square, he will just stand on a pile of flaming rubble behind Elda without doing anything. This can be fixed by skipping away from Windhelm and coming back, so it will be rebuilt, and re-initiate 'Patrol Windhelm at Night'.
 * Sometimes after completion of the quest, even if you caught Calixo and saved Arivanye she may randomly turn up dead at the stables or around Windhelm.
 * Sometimes after investigation Hjerm, Calixto is untraceable, making it impossible to sell him the amulet. Nevertheless you are still able to finish the quest by talking to Viola Giordano. Finding the real killer is also still possible as when talking to Jarl's steward your replies are as if you have talked to Calixto.
 * It is possible that Calixto attacks the woman on the market during the day. So keep your eyes open if you want to save her.
 * Purchasing Hjerim before officially starting Blood on the Ice will drop you about midway through the above timeline once you visit your house for the first time, skipping over the murder scene in the graveyard. This also occurs if you pick the lock and enter the house out of curiosity. Simply investigate everything in the house, making sure to grab both Butcher Journals, and bring one of the pamphlets to Viola Giordano. She will tell you to talk to the Jarl's steward, at which point you can choose how to end the quest. Note: You will not be able to purchase any decorations for your home until after the quest is completed.
 * Purchasing Hjerim before midway through Blood on the Ice will drop you in the above timeline just after the murder scene in the graveyard involving Calixto. You will not be able to kill Calixto Corrium to catch the killer. After you talk to Jorlief in jail and he tells you to patrol the streets, Calixto Corrium will run into Hjerim and will attack you whenever you enter. You will not be able to kill him, but he will stop attacking you if you do enough damage to kill him. Attacking him a second time will cause a bounty which will be removed if you subdue him. The quest is in-completable after this bug. Workaround for this Bug: Console Command "setstage ms11 150" will complete the step "catch the killer". After you talk to Jorlief to complete the Quest, Calixto Corrium is gone.
 * After you talk to Wuunferth in jail and he tells you to patrol the streets, Calixto Corrium will run into Hjerim and will attack you whenever you enter. You will not be able to kill him, but he will stop attacking you if you do enough damage to kill him. Attacking him a second time will cause a bounty which will be removed if you subdue him.
 * Sometimes after Wuunferth is imprisoned and you have waited several days, he will still not give you the option of finding the real murderer, but only the option to teach to you destruction magic.
 * If you kill Viola Giordano then purchase Hjerim, the quest will start but be incompletable, and you will not be able to purchase the upgrades for the house.
 * When picking up the pamphlets in Hjerim, the game will act as if you picked up the amulet as well, allowing you to talk to Viola about it as if you'd already identified it.
 * If you accuse the magician before you speak to Calixto it will complete the first part of the quest, however you can not remove the amulet from your inventory. The new quest tells you to capture the butcher, however, he is immortal and the quest does not end.
 * After you accuse the magician and you permanently have the amulet, you can wear two necklaces at once by equipping a necklace, then the pendant (so you will have the amulet and the necklace equipped), and then equip the second desired necklace.
 * If you pickpocket Calixto and search through his chest in the House of Curiosities you will find another journal entry of the Butcher. But don't worry, even though you already know who the killer is you will still have to follow the quest line as is.
 * Work around solution find a Nord named Tova. She will most likely be at the "House of Clan Shatter-Shield" go to that house at night pick the lock (Master) then go to the left room where she will be sleeping (inconsistent where she is) pickpocket her and grab the "Hjerim" key then go to the Hjerim house go to the left you'll see a bloody chest open it grab the "Butcher Journal" then the quest should trigger.
 * If you don't accept Calixto's offer to buy the amulet, it stays flagged as an undroppable and unsellable quest item, further clogging your inventory. Furthermore, it carries no enchantment, unlike if you sell and then retrieve it from Calixto's corpse. For a solution to this issue on the PC version open the console and type Player.additem 000D2328 -1, It will remove the strange amulet from your inventory.
 * Occasionally when you purchase the upgrade to "clean up that killers mess" for Hjerim, it may not actually clean it up. Reloading a previous save seems to fix it.
 * Finding the Butcher's journal in Calixto's house before starting the quest seems to prevent you from starting it.
 * Numerous weapon mounts on the wall and even the weapon rack may be seriously glitched when you buy Hjerim and fully decorate it. You will be able to take equipment off it (e.g. swords and shields) but you will not be able to display anything. In order to fix this, the player must complete both halves of the quest, meaning accusing the court mage and then finding out the actual killer. The player must also be Thane of Eastmarch before fully decorating the house. If the player decides to take the shortcut for the quest, which is confronting Wuunferth instead of speaking to Jorleif about the killer, the weapon rack and weapon mounts will be glitched.
 * If you choose the path to confront Wuunferth and Arivanya is dead, the quest will break right after Wuunferth tells you to patrol the Stone Quarter as she is the next victim. She will need to be resurrected before confronting Wuunferth.
 * On some occasions when Calixto runs to Hjerim, after being caught, the marker on the map says that he is outside the city walls. In actuality, he is not and for some unknown reason if the follow your local map it indicates his true location which is Hjerim.
 * Viola Giordano is not an immortal NPC if she dies at anypoint before the mission is complete the mission becomes stuck.
 * Occasionally, the body will not spawn at the start of this quest, and can't be seen until it's in the Hall of the Dead. This has no major effect on the questline though, since you do not have to interact with the body.
 * During the second half of the quest when you go back to speak with Wuunferth about the real killer the quest objective to search for the killer in the Grey Quarter at night will be given then almost immediately it will say the objective is completed no matter what time of day before going on to give the objective of catching the killer. Upon leaving the building Calixto will be seen running through the city and if the player attempts to stop him in any way he will call for help and the Windlhelm Guards will come to his defense. If allowed to escape Calixto will eventually make his way to Hjerim where he will be hiding in the room hidden in the wardrobe and no matter what the player does he cannot be killed, only hit until he crouches upon the ground begging for mercy before standing up and attacking again. He will not leave Hjerim and since he cannot be killed the quest will not end.
 * Sometimes the Windhelm guards will enter the house and attack the player while they attempt to subdue or kill Calixto even though they have not seen the attacks and there is no bounty on the player's head.
 * After you start the quest if you happen to walk by Hjerim before you ask for permission to investigate the murders your quest will update to "gain access to Hjerim". When this happens the guard that you must talk to (after getting the "ok" from Jorleif) will not be at the crime scene, therefor you will not be able to "Examine the crime scene" but you will skip to the part where you must enter Hjerim and continue the quest from there.
 * Sometimes Jorleif will not have the option to continue the quest after you speak to him about letting you investigate the crime scene. If you continue on with the quest and do everything as normal you should be able to complete the quest even though you it still says you need to talk to him for assistance.
 * Even if you discover the Butcher's Journal in Calixto's house after pickpocketting him during the quest and opening his chest, you will still need to wrongly accuse the courtmage of the murder before you can catch Calixto.
 * Sometimes Calixto will be frozen in the market with knife drawn behind Arivanya and is easy to kill with one hit but the quest will continue as normal
 * After completing the quest the amulent will stay in your inventory and can't be removed sayng it is a quest item.
 * The quest can be triggered manually even after finishing Imperial Legion questline. As Windhelm guards are now replaced by Imperial soldiers there will be no guard stopping you while passing around dead body at the cemetery. So you have to pickpocket Hjerim's key from Tova Shatter-Shield (you can do this at night while she's sleeping at her house - House of Clan Shatter-Shield). Then you visit Hjerim. When you enter, Blood on the Ice quest should activate. Now, you have to follow the quest. You accuse Wuunferth to be the killer. As Jorleif's going to arrest him with Imperial soldier, follow them to see where jail is in Blue Palace (you will need to know it further in future). Now the first part of quest is completted. You have to leave Windhelm for 3 days. When you come back another murder had place. You can find dead altmer body next to the Candlehearth Hall. Now, you have to go to jail in Blue Palace, open the door on cell where Wuunferth is. Speak to him and inform him that another murder had place in Windhelm, follow the dialogue and as you do so, second part of the quest should activate. Then just follow the quest to its end.(VERIFIED FOR PC)