The gender of the reindeer in the Rudolph story is determined by their names. The male reindeer have names that end in "er" (Dasher, Dancer, Prancer, Vixen, Donner, Blitzen, Comet), while Rudolph's female love interest is named "Clarice".
Is Dancer the reindeer a girl?
It's a common misconception that Dancer is a female reindeer in the Rudolph story. Dancer is actually male.