For now, we'll confine ourselves to the non-flying type. More about flying reindeer later in the series.
Reindeer (Rangifer tarandus) vary considerably in colour and size, with both genders growing antlers. There is some debate as to the gender of Santa Claus' reindeer. While both male and female reindeer grow antlers, males loose theirs at the end of mating season (early December).
This would suggest that all of Santa's reindeer must be female. Indeed, except for Rudolph, there is really no indication in their names to sugest otherwise. Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner and Blixen could all refer to females rather than males.
A reindeer's antlers are unique to the individual animal, just as fingerprints are unique to humans. This allows them to be tracked and monitored in the wild and in parks.
In terms of surviving in cold conditions, like the North Pole, the reindeer has hairs which are hollow in order to trap air and increase their bouyancy, thus allowing them to swim.