Hello.

Basically, you wait for Halloween. When Halloween arrives, the Big Zombie Deer (normally referred to as BZD) arrives into the forest. If you want zombie antlers, you need to cast the antler spell on him. That will result in you getting the zombie antlers for yourself. Same applies to the skull mask (cast mask spell on him) and the zombie pelt (cast pelt spell on him).

Normally he arrives a few days before Halloween and stays a few days afterwards, but that's all up to the gods.
You can normally tell when he's around as there's fog in the forest and if he bellows, you're sure to hear it.

Hope this helped!

(Of course, there are some players who might be able to cast them for you, but this is the official way to get them)