Who is Parson Brown?

In the lyrics of Winter Wonderland, I have often wondered who Parson Brown is... So I decided to investigate :)

Well all I could really come up with is Parson Brown is a fictitious name; however, Parson on it's own refers to a 18th or 19th century parish priest. Apparently each town wouldn't have their own priest so the priest would make rounds to marry people.
Interesting!!

Here are the lyrics for your enjoyment!

Sleigh bells ring, are you listening,
In the lane, snow is glistening
A beautiful sight,
We're happy tonight.
Walking in a winter wonderland.

Gone away is the bluebird,
Here to stay is a new bird
He sings a love song,
As we go along,
Walking in a winter wonderland.

In the meadow we can build a snowman,
Then pretend that he is Parson Brown

He'll say: Are you married?
We'll say: No man,
But you can do the job
When you're in town.

Later on, we'll conspire,
As we dream by the fire
To face unafraid,
The plans that we've made,
Walking in a winter wonderland.

In the meadow we can build a snowman,
And pretend that he's a circus clown
We'll have lots of fun with mister snowman,
Until the other kids knock him down.

When it snows, ain't it thrilling,
Though your nose gets a chilling
We'll frolic and play, the Eskimo way,
Walking in a winter wonderland.