This is a post to counter the Stormcloaks and to explain why I think Skyrim cannot survive without the Empire. Feel free to correct me or counter my arguments if you think I'm wrong!!
First of all is trade. Were Skyrim to secede from the Empire, it would lose most if not all of its trade with Cyrodiil and the other Imperial provinces. That leaves them with the Elves and Beastfolk, both of which Ulfric would be reluctant to trade with. The only Elven province that could trade with Skyrim is Morrowind*, and I doubt either nation would even consider it. The other Elven provinces are controlled by the Dominion, and trade with them isn't even worth thinking about. Skyrim could perhaps attempt to trade with the Beastfolk; but Argonians are pretty isolated and don't really do trade, and the Khajiit are ruled by the Thalmor. That leaves the orcs and the Redguards. The Orcs don't have much so trade with them wouldn't be all that prosperous. As for the Redguards, they might help a little, but their intention isn't to wage war on the Aldmeri Dominion. If it had been, the Second Treaty of Stros M'Kai would never have been made. The Redguards are more concerned with keeping the Thalmor out of Hammerfell, and so would not want to do anything to provoke them, meaning that if Hammerfell did assist Skyrim, it would be limited.
And so, Skyrim's economy would fail. This would leave Ulfric with no money to fund soldiers, and no nation to borrow money from. Also, many soldiers will have died and been injured in the war, and many people who fought in the war would quit and return to their normal lives. Furthermore, the war wouldn't be completely over. There would be resistance across Skyrim, which could very probably lead to another war. This state of a crumbling economy and a civil war would leave Skyrim pretty much free for the taking for the Dominion. Oh, but at least everyone could worship Talos before the Dominion comes and slaughters them.
Finally, let's just look at the kind of man who would be ruling Skyrim. Ulfric Stormcloak was tortured by the Thalmor during the Great War, so mentally he's pretty unstable. And remember the Markarth Incident? According to some sources, when Ulfric took the city, he executed anyone old enough to swing a sword who didn't fight at the gate to retake the city. We're talking twelve year old boys being beheaded because they were scared of fighting in a battle. Is this the kind of king Skyrim deserves, one who happily slaughters the the people he claims to love so much? Ulfric and his Stormcloaks fight for Skyrim's traditions; but Ulfric's idea of tradition is where all of Skyrim is willing to die for their king just because he's their king- the blind worship of a king or queen.
So to summarise, I think it's remarkably clear that Skyrim will fail as an independent nation. Skyrim has relied on the Empire for too long to be able to survive without it. The Empire doesn't love the Dominion as the Stormcloak seem to think. They just want to live to fight another day. Ulfric may be content with dying bravely and yet failing horribly, but that doesn't mean all of Tamriel is.
*I'm not sure if Morrowind is an Imperial province in the 4th Era.
These arguments came from taking to NPCs, reading books and my head. Hope I convinced you!!