If a creature you control enters the battlefield with a hat sticker on it, Haberthrasher's triggered ability will trigger twice.

A hat is a garment worn on the head that's not part of another garment. Hoodies, for example, are not hats. Items that cover only the face and not the top of the head, such as a face mask, are also not hats. Hats are purposely decorative. Simply balancing a thing on your head doesn't make that thing a hat.

Key in this set—space helmets are not hats, although some creatures with space helmets also are wearing hats underneath those helmets.

Wigs and headbands count as hats. There are wig and headband stickers.

The above information pertaining to hats for creatures also pertains to actual hats for players.

A creature "has a hat" if the creature depicted in the art is in possession of a hat. That creature doesn't need to be wearing the hat. A background character such as a scale bird having a hat won't count.

You "have a hat" if you have a hat with you, not if you own one somewhere. You don't have to be wearing the hat. But if you have a hat with you, why wouldn't you be wearing it? Does it not fit? Is it for a sports team that's bad? Did you just get your hair done? We're just curious. You don't have to explain.

You're "wearing a hat" if you're wearing a hat.

No player can remove another player's hat. That's unsporting conduct.