my yearly reindeer rant: both male and female reindeer grow antlers in the summer each year but male reindeer drop their antlers at the beginning of winter, usually late November to mid December. Female reindeer retain their antlers till after they give birth in the spring. Therefore, according to every historical rendition depicting Santa's reindeer, every single one of them, from Rudolf to Blitzen ... has to be a female.
In the old nature religion (in which the divine was often perceived as feminine) it was the female horned reindeer who reigned supreme as the great goddess of the winter solstice. http://gathervictoria.com/2014/12/04/doe-a-deer-a-female-deer-the-spirit-of-mother-christmas/
Deer: Family: Cervidae, Order: Artiodactyla, Class: Mammalia; even-toed ruminant mammals; include white-tailed deer, mule deer such as black-tailed deer, elk, moose, red deer, reindeer (caribou), fallow deer, roe deer, pudu, chital; male deer of all species (except Chinese water deer) & female reindeer grow and shed new antlers each year; differ from permanently horned animals such as antelope (in same order as deer)
Although antlers may be considered a masculine symbol, goddesses and female shamans wear them. Deer women appear throughout world mythology. Bendis, Artemis, Elen of the Ways, Satet, and many reindeer goddesses. Female reindeer, btw, have antlers and they are among humanity's oldest deities. (For the less spiritual, you can just enjoy this photo as a sexy Hannibal cosplay.)