I don't think you can call The Marvellous Toy a Christmas song, even if it does get played a lot at Christmas.

Another one I associate with Christmas is Scarlet Ribbons. It doesn't mention Christmas or Santa Claus, but I always assumed the ribbons came from Santa, for some reason. Does anybody know for sure where those ribbons came from?

I also associate the Seekers' version of Morningtown Ride with Christmas, because it was (IIRC) a big UK hit at Christmastime, and I guess it has the 'child appeal' lyrics of the above two songs.

Are there any other songs that are not Christmas songs, but people associate with Christmas?