From the Super Mario Wiki
Chill Bully is a Big Bully found in Super Mario 64 and Super Mario 64 DS. It has a light blue body and a single golden spike on the top of its head (as opposed to the usual black surface and twin horns of normal Bullies). Chill Bully appears in the 10th course, Snowman's Land. In this level, Chill Bully walks around on an ice platform above a pool of extremely cold water; touching this water has similar effects to touching lava. When Chill Bully is defeated, he releases a Power Star.
Unlike other Bullies, Chill Bully can be defeated in the DS remake by having Yoshi obtain a Power Flower and pushing it off the platform with his fire breath. This is most likely due to its icy nature.
Notably, Chief Chilly is very similar to the Chill Bully in design and behavior.