Canadianlefty, they don't grow velvet. The horns shed each fall around the end of October on in to November. The horns are constructed of hair-like material (sort of like your fingernail.) When they shed it comes off as a sheath. In other words the horns are hollow inside. (see picture below) Underneath is bone with new hair growing. If you don't believe me, talk to any taxidermist that's worth a darn in your area and ask him about cleaning antelope horns and the skull/bone underneath for mounting. I live in the heart of antelope country and in 10 years I have found a grand total of 4 antelope sheds. They deteriorate quickly and near as I can tell little critters love to eat them.
If you really want to know more go to the site I borrowed the image from. It has a good article all about antelope. Here is a link to the article.