According to the Alaska  Department of Fish and Game, while both male and female reindeer grow antlers in the summer each year, male reindeer drop their antlers at the beginning of winter, usually late November to mid-December.  Female reindeer retain their antlers until after they give birth in the spring.

Therefore, according to every historical rendition depicting Santa's reindeer, every single one of them, from Rudolph to Blitzen, had to be a girl.

We should have known.  Only women, while pregnant, would be able to drag a fat man (who would NEVER ask for directions) in a red velvet suit all around the world in one night and not get lost.