It will allow the antlers to "dry out" and shrink to their smallest size. That way, all antlers are being measured in the same state. A "green" antler that is fresh out of velvet will have greater size than a dry antler.
You can if you have a refrigerant dehumidifier that is connected to your central air system. Otherwise, you'll need to use a portable dehumidifier to remove moisture from the air.