I know there aren't that many, but at least there's a few. I'm not including games that take place during the calendar year either in real time (like Animal Crossing) or not (like Persona).
Christmas NiGHTS into Dreams: pretty self-explanatory, it's also included in the later console ports, although it's missing the cool presents you could get, including being able to play as himself.
James Pond 2: Codename: RoboCod: takes place in Santa's castle and you have to save Christmas.
Yakuza: surprisingly many of them take place at Christmas.
Daze Before Christmas: a platformer for the Mega Drive and SNES that's not particularly good.
Xmas Lemmings: basically demos of Lemmings with Christmas-themed levels, there were a bunch of these for PC and Amiga.
Tyrian: Originally a DOS shmup that was released as freeware and now has open source ports, there's a Christmas mode that activates if the system clock is set to December. I'm pretty sure there were other DOS games with Christmas modes too.
Duke: Nuclear Winter: a Christmas-themed expansion for Duke Nukem 3D.
RayForce is about as much of a Christmas game as Die Hard is a Christmas movie, but the true ending to RayCrisis reveals that Operation RAYFORCE saw the X-Lay launch on Dec. 24 MC 0185.
I wasn't expecting to see someone mention the Ray series* today, let alone in this thread. I'll count them as honorary Christmas games because I love them (I'm definitely never seeing the true ending of RayCrisis).
*Technically, the name for the series might be Ray'Z, because that's what the title of the recent collection used, but I think it looks stupid. You could say I'm not a Ray'Zist
Lifeline: unique PS2 game that you use a microphone and voice commands as your controls. You give voice commands and control a waitress aboard a rich space hotel that's taken over by aliens during Christmas time and have to survive. Also Mansplaining: The Game.
Blue Stinger: kino
Raw Danger and I think some of the Disaster Report games takes place during Christmas. Absolute cinema choose your adventure. A natural disaster befalls you and you must survive. Some of the choices you can make are absolutely psychopathic and funny lmao.
Parasite Eve is either a Christmas game or a New Years Eve game
PS2 and Dreamcast had amazing B-tier movie-like games that are Christmas games.
I also forgot that Batman: Arkham Origins was a Christmas game, and Jazz Jackrabbit 1 & 2: Holiday Hare, even though I had a list of games and that was on there.
I remember watching Yahtzee Crawshaw(zero punctuation guy) and friend(he once ate a spoonful of Gatorade powder) play that way back when. It's a weird game
Batman Arkham Origin
DKC3 there's a cheat to make every bonus level christmas themed with a very nice alternate music
Bully theres a christmas section or christmas DLC and the music is also banging