I guess this is not Santa Claus, those reindeer don't look like they will take off any moment. As a matter of fact this is a picture of a reindeer sleigh in Russia around 1900.
Can you name all of Santa's reindeer? Dasher and Dancer, Prancer and Vixen, Comet and Cupid, Donder and Blitzen. In 1823 the famous poem starting "'Twas the night before Christmas" was published anonymously. It has influenced the way we think of Santa Claus' appearance, his way of entering homes and giving gifts to children and of his means of transportation.
Let's not forget Santa's ninth reindeer, Rudolph with the red nose who entered the stage in 1939 in a coloring book.
I have to admit for me as a German it's a little sad that Santa and his reindeer start to come barging in like this everywhere now. I was raised believing in the "Christkind" (christ child) and I don't like to see local traditions die. Important is the spirit of Christmas, though, right ...