> (And before someone screams "citation needed," I'll just say that it's well known, and if you didn't know it by now, there's a thing called Google and Wikipedia that you can go look at.)

Lots of beliefs are "well known" and nevertheless wrong. Just look at all the people, even in this thread, claiming that Santa Claus was invented by Coca Cola, even though a simple google image search will reveal illustrations of Santa from before Coco Cola was founded. As for the pagan traditions around new years they are not very well documented and a lot is speculation.

Of course gift-giving is known throughout history, but the figure of Santa Claus is associated with the Christian celebration. I'm pretty sure you wont find any reference to Santa Claus or Father Christmas from before Christianity!