Parson Brown

I was listening to the radio as I was getting ready for school this morning and they played this jazzy version of "Winter Wonderland." Only maybe I shouldn't admit this because I don't come off looking so smart. Who am I kidding?  I'm no intellectual giant anyway. Anyway, they sang the part that says:
In the meadow we can build a snow man. 
Then pretend that he is Parson Brown.
He'll say, "Are you married?"
We'll say, "No man, but you can do the job while your in town."
For all of my 34 years I could never figure out what color parson brown was and what that has to do with getting married.  Only just this morning did I realized that Parson Brown was not a color but maybe a preacher.  In which case him being all nosey about marriage makes all kinds of sense!