Well, he is inspired by a saint, so that isn't terribly surprising. It's a bit convoluted how they got from Saint Nicholas to the current depiction, but... well, he's something of a composite figure. Some would suggest that he's also partially inspired by the pagan god Odin, who superficially resembles him rode through the sky on an eight-legged horse.

The reindeer were a flight of fancy by an American who wrote a poem that introduced several of the famous elements of his mythos. I believe they were included because they live in cold climates and, thus, well suited to traveling in cold weather.