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).
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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.
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Yakuza: surprisingly many of them take place at Christmas.
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Daze Before Christmas: a platformer for the Mega Drive and SNES that's not particularly good.
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Xmas Lemmings: basically demos of Lemmings with Christmas-themed levels, there were a bunch of these for PC and Amiga.
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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.
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Duke: Nuclear Winter: a Christmas-themed expansion for Duke Nukem 3D.
Blue Stinger for the sega dreamcast is as far as I'm aware the goat of Christmas games. Just look it up on youtube and bask in the weirdness.
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