Nice post, The male reindeer in the wild naturally lose their antlers at the end of the rutting season (Late Autumn) as they no longer need them once they have bred. The females however, lose theirs in the Spring after they have given birth to compete for food over the winter months. This means that Santas Reindeer are either Female or they are Castrated males. The castrated males will keep their antlers until injected with Testosterone in the New Year and lose their antlers between March and May.

Only Santa knows the overall answer to this question but I would personally say they are castrated males as their antlers always appear to have no velvet on them in Christmas cards!