I don't think it's necessarily winter that can get me down, as I actually enjoy winter for the most part. I like the quietness, the snow, the brisk cold.
I also enjoy rainy days on occasion. It's great weather to curl up on the couch with a cup of hot chocolate and read.
That being said, I have found that when I'm in a bad mood and the day is cloudy/rainy/cold, it does seem to worsen it. Sometimes during spring or fall if I'm in a bad mood, I can go for a walk and the nice weather will help cheer me up a bit. I suppose that's why it could be worse in the winter.
I also don't know if it's worse when you're single because I've never not been single so I can't say that I know.