Chill Bully

The Chill Bully is a variant of the Big Bully that appears in the Snowman's Land course. They appear in all versions of SM64, including the DS remake, though a different appearance as seen here.

Behaviour
The Chill Bully acts the same as a Big Bully, and drops a star when knocked into icy water.

There isn't a difference in behaviour, and thus, The Chill Bully is more of a texture/model swap of The Big Bully, who appears in Lethal Lava Land. However, unlike the Big Bully, the Chill Bully has a single horn on its head, preventing Mario from jumping on its head to push it back.

Dual Horns
Supposedly, the Chill Bully can have two horns like its normal counterpart. This makes it easier to defeat, removing the challenge.

Trivia

 * Appearances of both The Chill Bully and The Big Bully can differ between copies.