Okay, here's my list, bolding ones that didn't make it:
01. A Christmas Carol (Tom Lehrer) [Oldest parody carol I know by far, mostly holds up]
*02. Chiron Beta Prime (Jonathan Coulton) [Nothin like a good SF dystopia xmas]
03. White Wine in the Sun (Tim Minchin) [Explains how I feel about much of the rest of this list]
04. The Christians and the Pagans (Dar Williams) [Another great one along similar lines]
*05. Peace on Earth / Little Drummer Boy (David Bowie and Bing Crosby) [Amazed that this thing exists]
*06. 'Zat You, Santa Claus? (Louis Armstrong) [Can't say no to having Louie on the list]
07. Santa's Beard (TMBG) [Rockin tune, disturbing lyrics, par for the TMBG]
~08. Feast of Lights (TMBG) [Hey look, a Chanukah song not by Adam Sandler]
09. Super Mario's Sleigh Ride (the OneUps)
10. Twinkle Twinkle Holidays (Yoko Shimomura)
11. Carol of the Final Fantasy Belles (Jay Epperhart)
*12. My Favorite Things [kinda tangentially Christmas]
*13. Carol of the Bells [Let's get Ukranian up in here]
*14. Feliz Navidad [Let's also get Latin up in here]
15. Oh Little Town of Bethlehem [TBH I just love the chord progression in the bridge]
16. O Come O Come Emmanuel [more fun chord progressions in this one]
*17. O Holy Night [this one's real fun to sing]
*18. Have Yourself a Merry Little Christmas [I'm from St.Louis, see]
*19. Christmas Eve/Sarajevo 12/24 [An arrangement of two other songs on the list, but what an arrangement]
*20. Jingle Bells [Eh why not. Fun if you have actual sleigh bells]
21. Sleigh Ride [Also fun with actual bells]
*22. The Twelve Days of Christmas [fun at parties]
*23. Tchaikovsky's Nutcracker [The whole thing, why not]
*24. What Child Is This? [Really I just like Greensleeves, and yes the chord changes trip me up]
*25. Grandma Got Run Over By a Reindeer [Not as old as the Lehrer, but still a parody classic]
Pretty high hit ratio all told. 9-11 are winter holiday themed *remixes* of game music, mostly from over a decade ago, that were gonna take some serious luck to match up with anyone else. Was curious if anyone else would hit the atheist Xmas tunes I had at 3-4. And here's my long-shot #1; it's honestly a pretty generic "Xmas sure is commercial these days innit?" parody, but it's a pioneer of the form so I thought it deserved some recognition.