Santa's main animal helpers are the reindeer, and they also don't date back all that far, their first known appearance being in "A Visit from St. Nicholas." The poem also established their names, although I understand that the earliest versions refer to the last two as Dunder and Blixem. I'm not sure whether the reindeer or Santa's Arctic home came first, but I know some sources referred to his home as being in Finland, before his residence at the North Pole was established. Baum placed Santa in the Laughing Valley of Hohaho, rather than at the Pole, but kept the reindeer. In his version, there are ten, and their names are different from the ones we all know today.
That Santa is married is also a pretty new idea, which makes sense, because why WOULD a Catholic bishop be married? Besides, the popular name "Mrs. Claus" is kind of absurd, as "Claus" wasn't intended to be a surname. At least according to Wikipedia, Katherine Lee Bates introduced "Goody Santa Claus" in a poem that she wrote in the late nineteenth century. Some European countries have traditions of women who fulfill the same basic role as Santa, like St. Lucy and La Befana, but a female counterpart is hardly the same as a spouse. Mrs. Claus's role in popular culture is probably largely due to her appearance in several of the Rankin-Bass specials. In Santa Claus Is Coming to Town, her name is Jessica, and she has a psychedelic freak-out upon realizing she's in love with Kris Kringle.
I'm hoping to focus on Jack Frost and Father Winter next weekend, and then the Saturnalia after that. Stay tuned!