I thought of another "Christmas song" that does not mention Christmas (or Santa or reindeer or the like):

Home For The Holidays

And there's a similar one called "Happy Holidays," but I don't know all the lyrics to that one off the top of my head, so I'm not sure it doesn't mention Christmas.

And a song that's become associated with Christmas but which isn't really about the holiday (much less anything religious) is the Victor Herbert song "Toyland."

Tom Paxton's song "The Marvelous Toy" is also sung a lot and played on radio at Christmas time.