The reindeer is a source of life for the nomadic Laplander tribes of the arctic. Because the reindeer sometimes eat the psychotropic toadstools known as amanita muscaria (fly agaric, which is also poisonous--flying reindeer?), these animals are also valued by Saami shamans who, in visions, soul-journey on the backs of reindeer, or through the chimneys of their homes. In Hans Christian Andersen's The Snow Queen, little Gerda sets out on an almost shamanic journey, on the back of a reindeer, to rescue her friend Kay.
As for Santa Claus, he may have originated from fertility deities such as Holland's Black Peter, who carried a sack full of babies to deliver, in the new year, or the Nordic fertility god Freyr, who was king of the elves.