Reindeer

Reindeer were a mammalian species. Santa Claus sent a sleigh pulled by reindeer to the First Doctor, John and Gillian to take them to his house. (TVC: A Christmas Story)

Behind the scenes

 * A reindeer was a "special guest" in several short, non-canonical promotional videos produced for BBC One in 2009 for broadcast at Christmas of that year. The spots feature David Tennant, in character as the Tenth Doctor, cavorting in a snow-covered forest with the TARDIS and a reindeer. In the longest video of the promotion, the Doctor hooks several reindeer up to the TARDIS, and they take flight (suggesting they are flying reindeer like those used by Santa Claus). Two short "sting" promos of about ten seconds each show a single reindeer wandering outside the TARDIS.
 * The promotional videos are not part of continuity, though they were included in a DVD/Blu-Ray box set release of the 2009 Specials scheduled for early 2010.