Here's a stab at this...going from one extreme to the other...
Who remembers this one?
"I Want a Hippopatamus for Chrismas" - The Three Stooges
(although probably made more infamous by Gayle Perry).
Then there is the one by a female group (from the 80's, I think) "Christmas Wrapping" - The Waitresses.
Also, "Father Christmas" - The Kinks.
And to add a bit of Texas flair to this thread:
"Pretty Paper" - Willie Nelson...always a classic at our house...
I also have the Brian Setzer Christmas album...have to find it again and give it a critical listen...pretty fun though from what I can remember.
Best version of "Baby, It's Cold Outside" I've heard was by(strangely enough) Whoopie Goldberg and Harry Connick, Jr.
There is also a version of "The 12 Days of Christmas" that I heard on Doctor Demento a number of years ago..."Rigging up the lights..." with someone doing a bad Paul Linde impression as one of the days...
And who can forget the unforgettable "Chipmunks Roasting On An Open Fire"...
Okay, I'll stop.
WhatFurrer