Well you are half right, you see all deer (cervids) go through an antler cycle. The cycle is almost identical regardless of species, this "velvet" as it is called is actually the vascularized tissue of the antler as it grows. The antler then begins to mineralize and work outward and eventually the velvet is shed by the deer but as it is still vascularized it does bleed. The antlers velvet and grow most of the year and then, depending on the seasonality of the deer, their testosterone spikes and it causes the mineralization process to begin and for deer to put on weight for rutting. Rutting is when male deer compete over mates through fighting and the use of their antlers. The testosterone then bottoms out and the antlers are shed before the winter sets in and they begin to grow again as velvet. They will continue to grow until the testosterone spikes again. However, if you castrate a deer, it will continue to grow antlers indefinitely and they will never mineralize and shed. This of course leads one to the realization that if santa's reindeer have antlers in winter, they are all castrated males... damn santa that's cold

Edit: Female reindeer can also have antlers during the winter but they are smaller and are only present if the female has calved that year and has something to protect