Came accross an interesting site that pondered the issue whether Rudolph - he of the red nose - is, in effect, a female! I suppose there's no law that states Rudolph couldn't be Rudolphia and that eight "tiny" reindeer have to be male. It would infer that a certain jolly old gentleman could be sexist.
Actually, there has been very little (if any) discussion or examination revolved around whether this could be/might be a possibility. According to the Wildlife Notebook series - Alaska Department of Fish and game, Santa's Reindeer (R.t saintnicolasmagicalus) look very similar to common reindeer or caribou! Could there be a cover-up afoot or ahoof? However, Santa's guys (or gals) have many characteristics distinguishing them from seven sub-species including the genus from Finland, Greenland and other places accross the globe where reindeer reside. This is a topic that would get a great discussion going while drinking egg nog.
Now we all know and accept that Santa's reindeer live at the North Pole and are catered to by Mr. and Mrs. Claus and some elves. Furthermore according to the piece, the R.t saintnicolas magicalus (a specialized breed obviously), they're not listed on the endangered species list. Whew - thank goodness!
It appears that both male and female of the species have antlers. Go figure! It has been generally accepted that only males grow them, ergo, Santa's reindeers are guys. However...the females keep the antlers until Spring (probably to use against overly-amourous bulls) and most bulls drop their antlers by early December. So the possibility exists that at least some of Santa's flock could be females! When you think about some of their names could be a clue like Cupid is definitely more feminine than masculin and Vixen and Prances could go either way.
Anyway, only Santa knows for sure and he's sure not telling!