The Headless Snowman is a minor snowman (and therefore possible Mr. Blizzard or Dr. Freezegood) character who appears on Cool Cool Mountain of Super Mario 64 and Super Mario 64 DS. He resides on a pedestal around the halfway mark of the mountain.
Despite his name, the Headless Snowman has never been seen to be decapitated, although his body once melted away during the events of Super Mario 64 (in the stage Snowman’s Lost His Head, to be exact). Thankfully, Mario was searching for Power Stars on the mountain at the time and assisted the snowman (who was looking for nearby headhunters) by rolling down a huge snowball fit to be the Headless Snowman’s new body. The happy snowman gratefully awarded the hero with just the thing he was looking for: a Power Star.
So don’t forget to give the snowman both it’s head and body!
By Supermariofreak, info from Mario Wiki