Reindeer are the only species of deer in which both males and females grow antlers. Females usually retain their antlers until the spring, so as to protect scarce resources during the winter, while males typically shed them in late autumn.
The same goes for caribou, the North American version of reindeer, which are the same species. Caribou tend to be a bit larger than their “old world” cousins, and are domesticated less frequently, if at all.
Reindeer employed to pull sleds are almost always castrated males, with antler cycles similar to those of females. That explains why Santa’s reindeer, including Rudolph, still all sport antlers in December. In habitats where food is especially hard to come by, some females forgo growing antlers in order to conserve energy.
Photo credit: Alexandre Buisse (Wikipedia Commons)