They do when they’re growing, it’s a covering called velvet and it’s rich with blood.
The velvet is on the out side of the antler. It’s a thin layer, that’s all.
When the antler is done growing it begins to loosen up and the buck will rub it on trees to get the velvet off.
The buck will sometimes eat the velvet.
The antler itself is dry and the inside does not have a blood supply.