Seems to me that the right parson to marry a snowman to a snow-woman would be a snow-parson. I'll help you build him.
9 seconds sound clip from the Frosty's Winter Wonderland movie soundboard.
You can hear this line at 00:15:13.946 in the Blu-ray version of the movie.
Quote context
[...]
- A wedding? We're going to need a preacher. Come on.
- They were going to hold a wedding that very night.
- Finally, Parson Brown showed up, but when he saw Frosty and Crystal...
- And so they all pitched in, and one, two, three, there was the nicest snow-parson you ever did see.
- And then, to make him all living...
- A parson's not a parson till he holds the good book in his hand.
- A wedding? Aww. Now the competition will be double.
[...]