This will be a "Public Domain Version of 'Rudolph the Red-Nosed Reindeer' That Pops Up Everywhere"-Free list of old Christmas cartoons. :)
Hugh Harman's "Peace on Earth" - I'm going to start by posting the animated short first:
Now, this short is beautifully animated and notable (even admirable) for its pro-peace message delivered in the middle of wartime. But here's the thing: I first saw it as a little girl in the middle of a collection of more typical holiday cartoons. Let's just say I had a lot to think about while everyone else was eating cookies and singing "Jingle Bells."
Dave Fleischer's "Christmas Comes But Once a Year" - Everything is going to look like sunshine and lollipops after that last short, but this one's a little odd too. Mostly, it's because of Dave Fleischer's strange animation style. This is what Western Animation looked like before Disney came along and standardized everything. The special effects at the end are really cool:
The National Film Board of Canada's "Christmas Cracker" - I discovered this on NFBC's "Best of the Best" DVD collection, but the embed below comes straight from the Film Board's website. The animated segments range from the "aww how cute" to the "Augh I know I've seen this before!" The weirdness is provided by the jester MC and trippy version of "The Holly and the Ivy":
As a super-special-awesome bonus, here is the cheesiest/creepiest Christmas song and music video ever made: