In the story "Rudolph the Red-Nosed Reindeer," which was written by Robert May, there is no mention of how Rudolph's nose came to be red or glowing. Rudolph was taunted for his glowing red nose in the story.
In the story, none of the other reindeer play with the young buck Rudolph because of his glowing nose. It isn't until he proves himself useful that he is treated better by his fellow reindeer.
Rudolph the Red-Nosed Reindeer sold over 2.4 million copies in 1939. The story of Rudolph was put to music in 1949 by songwriter Johnny Marks, who was Robert May's brother-in-law. The song was recorded by the singing cowboy Gene Autry and the album sold 2 million copies in the first year.