Ideally at or below the PSP/N64 threshold so I can play it on my RG405M.
All I can really think of are ROM hacks for Super Mario Bros.
You might want to look into DOS or even Flash games. Can’t tell you what’s actually good, but I can tell you there’s a lot out there!
Maybe Lemmings would be a good starting point. I think they had a Christmas edition.
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For flash games, there’s the FlashpointArchive. It should have almost all the old flash games
The opening level of Batman Returns on the SNES is set around Christmas time with Christmas trees visible in the background. Not exactly what you were asking for, but it’s a good Beat 'em Up game.
I feel like that makes it as much of a Christmas game as it makes Die Hard a Christmas movie