I don't think they celebrated Carnevale during the Black Plague. But it's not really a question of "would they do it", it's a question of "would a holiday thematically distract the player from the overarching dark and gritty theme". Would they celebrate Christmas in Fallout 3? The ruins of DC could certainly use a little cheering up, but that really breaks the feel of the game if you include something that contrasts with it so much.
However, if there are big cities that are overall civil and tranquil, then holidays would work fine. I still need to see the game before I make a final judgment.
Well obviously it wouldn't have that renaissance feel that we've all seen before and which I hated about Oblivion. People are always looking for a way to raise spirits in dark times. It wouldn't even be limited to just holiday festivals. What about celebrating around a slain dragon in the town, or perhaps the rebel faction/pro Empire winning a victory? These can be meshed with other festivals to create atmosphere. Just because some people may know that Alduin is approaching doesn't mean that they're gonna shut themselves inside with despair. It's a morale thing. They might as well take out woodcutting and other job skills because people know that doom is upon them, so they would quit the jobs since that's a low matter at hand. Doesn't work that way.
I believe in your case that it should start happening at a certain point in the main quest, like after you visit High Hrogthar and the people of Skyrim have some sort of confirmation that you are indeed the Dovahkiin, giving them a shred of hope.