Au contraire, the image of "Santa" -- a Saint -- has been around for a long time. He's been part of the Xtian rebranding of Saturnalia since 1600 or befor (I'm pretty sure that even predates the Coca Cola Corporation -- citation needed).<quoted text>
While hares are seen as symbols of fertility, they don't really have a part in the "liturgy" per se. Santa is purely xian, invented for commercial reasons. It was an ad for Coke, IIRC...
St Nicholas, Sinterklaas, Tomte, Father Xmas ... all incarnation of the same person. Like Doctor Who with a sleigh instead of a TARDIS.
The good folks at Coca Cola have been using his image since the '20s and have probably done more to canonize his image as the morbidly obese, flamboyantly dressed, elf molester that we have come to know and love. But, they didn't invent him or his likeness.