As for all the reindeer (assuming that the common illustrations of them are acturate) being female -- This conclusion is not the punchline to a joke, but based on biology.

Reindeer are (iirc) the only antlered creatures where both the males and females have a set. The males drop their antlers in the fall, after the rutting season, but the females keep their antlers all through the winter.

Since all the reindeer shown pulling Santa's sleigh on Christmas eve still have antlers, they must all be female...