No no no, they're pretending that he's a parson. Someone with the ability to marry them. Like a sea captain.

But he's already in town, isn't he? Why not do it right away? No, I think they're making arrangements for him to perform "the job" on a recurring basis, which clearly couldn't refer to the sanctification of a marriage.

Jesus, Tom, it's so simple. They live in the town, they're talking about taking a romantic walk through the meadow (OUTSIDE OF TOWN IN A MAGICAL WINTER WONDERLAND), and they're so in love that when they stumble across a snowman, they'll start to have a conversation with the snowman as if he was a real person who exists named Parson Brown who could marry them at some point when they are back in town.

Hmm. Your argument about the location is unpleasantly convincing.

Sommer's explanation makes sense. I'd never understood that bit before. (In retrospect, it seems kind of obvious.)

No, no, no. Their stoned out of their minds (hence, the "no man") and definitely propositioning the parson.

This is why I enjoy being Jewish. They're no such confusion with the Dreidel Song. It's a dreidel. It's little. It's made of clay. The end.

He'll say: Are you married?
we'll say: No man

A transitional comma in the response would indicate a reply and to whom it was directed. Minus that comma, we should read what has in fact been written: an answer, a reasoning. These lesbian lovers can't marry! I do sympathize with their plight, but gender reassignment surgery seems like a rash solution if it's merely a legal problem that obtains, and anyway the surgery should be performed by a trained surgeon, not the first two-bit snowman huckster they come across.

Sommer nails it, although Tom can be comforted knowing that my wife had the same confusion most of her life.

I keep unintentionally wanting to mis-sing this as "And pretend that he is Alton Brown".

Okay, again, I think a little less Food Network over at the Flophouse might be a good idea.

I second Sommer's explanation; it's what I've always thought it to be. And I thought Parson Brown was an actual man of the cloth, but it looks like it might be a generic reference:

http://www.urbandictionary.com/define.php?term=Parson+Brown

Though, it's hard to give creedence to a definition that uses this song as its only example. Wonder which came first.

Of course, you can sidestep the whole kerfuffle completely by using this version:

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 children knock him down

Though, they don't go into what kind of "fun" they'll have with Mister Snowman, still leaving open the possibility of impropriety.

Hey, who among us hasn't shtooped a snowman a time or two? It's all a part of growing up.