EDWARD SCISSORHANDS is not a Christmas movie, but is often counted as such since some of the tracks have a very Christmassy feel (and there are a couple of scenes that take place during Christmas).
So much so that Christmas commercials have been ripping off Elfman's score for many, many years now to evoke a sense of holiday wonder!
Depending on whether you consider it a "Christmas movie" or "a movie that takes place at Christmas," Gremlins fits the bill. Batman Returns takes place at Christmas and I think there is some non-score-related caroling, although I may be wrong about that as it's been a few years. The first "Harry Potter" has John Williams' bizarre ghost Christmas song, as well as a very Christmassy piece that follows.
And the recent score to "Batman: Arkham Origins" takes place on Christmas Eve and perverts "Carol of the Bells" into a theme for the Joker.
Like the first film, Die Hard 2 takes place just before Christmas day and we hear Carol Of The Bells as John McClane is entering the airport terminal after his in-laws' car is towed away. It also has that wonderful airline crash scene to give us the warm fuzzies.
In the opening scene of CAST A GIANT SHADOW (1966) as James Donald tracks Kirk Douglas in Macy's store in NYC, it's Christmas-time! Cue : Elmer Bernsteinian renditions of "Deck The Halls..." and "Jingle Bells".