The juggernaut of prime time cartoons has outlasted the age of irony, post-irony, and colonial irony. Naturally most of its holiday contributions are parodies of carols (caroldies).
“The 39 Days of Christmas” (sorry about all the non-song bits) came after “The 12 Days of Christmas (parody).” “The Grinch (parody)” nobody remembers. (Get that poster a tripod for Christmas.)
Better are the Nutcracker bits.
The holiday-inspired “Everybody Hates Ned Flanders” is the winner here, by a single Homer hair. (I mean, David Byrne covering…!) [To discover why this is considered a carol, watch the poorly recorded 40 second intro here–then stop watching.]