There was his nose, to begin with. In the first version of “Rudolph the Red-Nosed Reindeer,” it glowed “like the eyes of a cat,” and Rudolph’s friends nicknamed him Ruddy because of it.

A red-nosed reindeer might not be as unusual as you think. Rudolph the Red-Nosed Reindeer is a Christmas icon, immortalised in books, songs and films. But the cause of the beloved cervid's crimson ...