Sneaking on a chest that's on an ice block doesn't prevent you from falling off the side.

If you place a chest on an ice block, then go on the chest and sneak (hold shift), you can still fall off the side of the chest.

I think this happens because the chest isn't as tall as a regular block, so you can slide on it as if the chest were ice. The sliding may have something to do with falling off the side.