If it a annoys your that much, reload a save.
I think the hood is part of the Vampire Royal armor that she initially wears. Plus, Serana looks better without a hood.
Serana's Hood is a separate item to the Vampire Royal Armor but they do seem somehow linked in the game code for Serana. I've given Serana a lot of loot to help carry and not once did she replace the hood or her armor (never gave her Dragonscale though) like M.Owen said if you removed the scale armor and she still doesn't use her hood you'll have to go back to a save before it happened. The general opinion of the internet seems to agree with Rigid Generic lots of people asking how to get rid of the hood no one wanting it back.
I actually gave her Dragonscale Armor in the past as well, but that didn't stop her from wearing her hood outdoors, so that busts the theory of a bug with Dragonscale armor or the theory that it's linked with the Vampire Royal Armor.
If it really bothers you, you could use console commands "equipitem XX00E6A0" (where XX is the placing of Dawnguard in your load order) to make her equip the hood outdoors, and see if that fixes it.