I don't know why, but doe is the name for female deer but in the case of reindeer the female is called a cow. Rudolph must be female as it is always pictured with antlers and only female reindeer would have antlers at Christmas time. Male deer would have shed their antlers by December but females shed theirs in spring and so would have grown theirs back by Dec. that info. comes from living next to a Safari park!!!
Found this on WikiAnswers which really confuses the issue.
Female reindeer are called does, male reindeer are called bucks, and baby reindeer are called fawns.
In Alaska, they call the females cows, males bulls or steers (if they are castrated) and babies calves.