Why do male deer get fuzz on their antlers?

That's the velvet that is surrounding the growing bone portion of the antlers. This velvet and antler regrowth which occurs every year for all species under the Family Cervidae, occurs from spring until fall, which is when the velvet falls off and rubbed off by bucks (or bulls, referring to elk, moose and caribou specifically) who are getting ready for the rutting season.