Reindeer

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

Encounters with reindeer
The Doctor, their 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 Smith met St Nick on a New York estate — an encounter which was witnessed by Clement C. Moore. (PROSE: A Visit from Saint Nicholas) The Tenth Doctor's TARDIS was pulled by reindeer after he discovered a group of them among the snow. (TV: The Doctor and the Reindeer)

In a dream, three reindeer, Rudolph, Donner and Blitzen, flew around Clara Oswald's home after Santa's sleigh crashed on the roof. Santa later rode into a polar base on Rudolph to stop the dream crab attack. Santa claimed to Shona McCullough that his flying reindeer were a "scientific impossibility", and as a result, he fed them "magic carrots" so they could fly. (TV: Last Christmas)

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)

According to one account, Santa's reindeer differed physically from normal reindeer, apparently being "a shade greener" in colour, and possessing at least two more legs. (COMIC: Frosty the Snowdemon)

Of course, not all encounters with reindeer were associated with Santa. The Eighth Doctor and Izzy Sinclair 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 illustrations — just as Jasmine Deering did in her advertising campaign for Blackstone soft drinks. (PROSE: Christmas in Toronto)

Information from invalid sources
A Christmas stocking was decorated with an illustration of a reindeer. (NOTVALID: 2016 BBC Christmas ident)