Is Santa a democrat or republican?

Hard to say.

He gives away all the toys his workshops make, so that would qualify him as a Democrat.

But his workshops are basically sweatshops, he doesn't believe the Federal Aviation Regulations apply to him, he commits breaking and entering millions of times every year and no animal welfare organization in the world would condone forcing eight or nine (depending on which version of the Santa myth you like best) wild animals to drag a sleigh full of toys all over the world in one night. That sounds pretty Republican to me.

But in reality it doesn't matter: he can't be either a Democrat or a Republican because the North Pole isn't U.S. territory.
He is most certainly a Democrat , because he is a fraud that takes credit for work done by other people (read UPS, FEDEX, USPS).