Rudolph (Last Christmas)

Rudolph, also known as Rudolph the Red-Nosed Reindeer, was one of Santa Claus' many reindeer who lived on the North Pole with Santa, the other reindeer and all Santa's elves.

During Christmas, Rudolph, two other reindeer Donner and Blitzen, Santa, his sleigh and elves Ian and the Wolf crash landed on the roof-top of the house Clara Oswald lived in.

Later Santa rode on Rudolph's back to the North Pole to help out the Twelfth Doctor, Clara and four scientists escape from dream crabs. When Rudolph acted up, Santa parked him with a key, which calmed him down and turned off his red nose. Later Rudolph along with Donner and Blitzen pulled Santa's sleigh with the Doctor, Clara and the three remaining scientists Ashley Carter, Shona McCullough and Fiona Bellows on board.

Rudolph could not fly by himself, so Santa fed him magic carrots. (TV: Last Christmas)

Other references
Rudolph had a popular Christmas song written about him. (TV: The Christmas Invasion, Turn Left

Behind the scenes
A rendition of the aforementioned song was sang by Strax in the non-valid webisode Songtaran Carols, during which he exclaims Rudolph's glowing red nose was a tactical disadvantage, as it allowed Strax to punch him in the dark.