The Doctor's fur coat

 was a fur coat used and worn by the Second Doctor in cold weather.

The coat was made of polyester rather than animal skin and was bought by einter the First or Second Doctor on the planet Thraxis. (AUDIO: No Place Like Home)

The Doctor was first known to wear it during his second incarnation, when visiting the Himalayas. He wore the coat to protect himself from the cold, but the coat lead him to being mistaken for the Robot Yeti who had been killing villagers. The Doctor was able to prove his innocence and stop the Yeti. (TV: The Abominable Snowmen)

The Doctor wore the coat again when encountering the Ice Warriors. (TV: The Ice Warriors)

The last time that the Second Doctor was known to wear the coat was when he visited his old friend The Brigadier in the 1980s. He and the Brigadier were captured and taken to the Death Zone on Gallifrey. He was able to take them home. (TV: The Five Doctors)

At one point, the Fifth Doctor stopped and studied the coat in the TARDIS wardrobe. (AUDIO: No Place Like Home)