I don't think it's possible to speed things up - I wish it was because I have the same problem, I have an eye illness which prevents me from being able to look at bright screens, so my TV screen is set to "very dark", and I see absolutely NOTHING during the night, especially not when it's foggy. I really dislike how long the nights are as well, it always seems like as if they slow down time during the night or something. I've lost count of how many times I've fallen down somewhere or crashed into a tree or got shot by an enemy just because I couldn't see where I was going or where the enemy even WAS. (Eagle Eye helps but not when you're trying to get away from something or someone.) I would love to be able to speed up the time so that it's always daytime for me in the game. I did that all the time in single player where you can just go to sleep.
MrPicard's post in Why is it night so often and so long was marked as the answer