The only Christmas-themed game level I've ever played (to my recollection) is Grubbins On Ice, the dlc for Costume Quest, but I can't say as I noticed the music.
As for favorite Christmas music, there's a lot I like. Mostly folk stuff that most people have never heard of and traditional carols and hymns. The stuff I tend not to like is the secular stuff, especially the stuff that's been given the modern pop treatment. It's kind of like someone scraping their fingernails down the blackboard as far as I'm concerned. I was planning on doing a Christmas music blog soon, so you can see what I do like when I write it.