Reindeer

Reindeer were a mammalian species of the deer family, often associated with Santa Claus.

Encounters with reindeer
The Doctor, his companions and acquaintances occasionally encountered reindeer — and, indeed, Santa Claus himself. Once, Santa sent a sleigh pulled by reindeer to the First Doctor, John and Gillian to take them to his house. (COMIC: A Christmas Story) On another occasion, the Third Doctor and Sarah Jane met St Nick on a New York estate — an encounter which was witnessed by Clement C. Moore. (PROSE: A Visit from Saint Nicholas) At Hyperville — Europe's largest shopping mall in 2013 — the Tenth Doctor encountered the Snow Queen, who, like Santa, chose to travel in a sleigh pulled by reindeer. (PROSE: Autonomy)

Of course, not all encounters with reindeer were associated with Santa. The Eighth Doctor and Izzy once met some Noxmycota-crazed reindeer when they visited Sweden in 1070. (PROSE: Illumination)

Cultural references to reindeer
Reindeer were so associated with Santa Claus that replicas were often made of them for Christmas decorations. The Tenth Doctor and Donna once landed at a "Santa's grotto" in a garden centre which contained large reindeer figures. (COMIC: Frosty the Snowdemon) Artists often included reindeer in their Christmas illustration — just as Jasmine Deering did in her advertising campaign for Blackstone soft drinks. (PROSE: Christmas in Toronto)

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 costume and 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.