Deck us all with Boston Charlie!
Walla Walla, Wash. and Kalamazoo!
That’s the beginning of of Walt Kelly’s spoof of Deck the Halls, sung every Christmas in his comic strip Pogo.
I also remember a schoolyard parody of We Three Kings:
We three kings of Orient are
Trying to smoke a rubber cigar
It was loaded and it exploded
Now we wonder where we are
Any others? I’m defining a Christmas spoof to be altered lyrics to an existing Christmas song, so forget about Grandma Got Run Over By a Reindeer … if you can.
The Mistletones do a number called Toy Sack which is a Christmas-themed parody B-52’s Love Shack. But that’s the other way 'round from what you are asking for, which is more along the lines of the classic:
Our own Doper brujaja has written a number of carol parodies related to Cthulhu. There are more than what I list here, but these will give you an idea.
We Three Things Abhorrent Are
It Comes Upon a Midnight Drear
On the Night Cthulhu Comes(Jolly Old St. Nicholas)
Cthulhu the Monster(Frosty the Snowman)
This one is one of my favorites
Tentacles Are Coming to Town
It’s not a spoof as such, but “The Christmas Boogie” by the Davis Sisters is a lighthearted and unorthodox rendering of Clement Moore’s “A Visit From Saint Nicholas,” done in a hip early 1950s space age style. Lots of fun.