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
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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.
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