who is parson brown in the christmas song

In the popular Christmas song "Winter Wonderland," there is a line that says "We'll have lots of fun if it doesn't snow, when Santa Clause gets his parson brown." The reference to "parson brown" is actually a bit of a mystery. Some people believe it is a nickname for a person, perhaps a pastor or other clergyman, who is supposed to be conducting a wedding ceremony on Christmas Day. However, it could also simply be a nonsensical rhyme that the songwriters used for the sake of the rhythm and melody.