A snowman was the titular character of the animated film broadcast as a television special, The Snowman, he flew around and danced with Father Christmas and other snow people. (PROSE: The Doctor on My Shoulder)
When the Tenth Doctor said goodbye to Mason Valentin, he said, "After all the flying around, having fun, and doing the impossible I've reali[s]ed something: I'm the Snowman and...time's up." (PROSE: The Doctor on My Shoulder)
Behind the scenes[]
The Snowman featured in DWM 213's Doctor Who? instalment as a "real" individual. He teamed-up with an Ice Warrior, a union that was later considered "unfortunate", and walked through the air with him and James.