Normally, both the female and the male reindeer grow and lose a new set of antlers every year.
The reindeer bull starts growing his antlers in March-April – and loses them after the mating season in late autumn.
The reindeer cow keeps her antlers throughout the winter – until after she has given birth in May-June. A new set is usually complete by late August.
The reindeer calves start growing antlers a month after they are born. In their first annual cycle, they keep them until early in the following year.
So yes, Santa Claus’s reindeer are probably all female – as they have antlers in December.
NRO.A.7.01