A sleigh was a means of transport.
Santa Claus sent a sleigh pulled by reindeer to the First Doctor, John and Gillian to take them to his house. (COMIC: A Christmas Story)
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)
In a dream crab created dream, the reindeers Rudolph, Donner and Blitzen flew around Clara Oswald's home after Santa's sleigh crashed on the roof. (TV: Last Christmas)