Contest may be too strong of a word, more just a game. Since articles with titles like this one don't get many views here, I don't know if I will get any responses, but, why not try. Can you name any holiday songs that are popular this time of year that make no reference to Christmas (this would include religious songs) or related Christmas characters? So, nothing about Santa or such.
So, a couple to get you started:
Baby, It's Cold Out.
If you have anymore, leave them in the comments. Just to make it sorta of like a contest, I will follow anyone that does comment. Thanks for playing.