A song that begins "O, the snow it melts the soonest" is printed (without a title) as part of an article called "Letter from Mr. Shufflebotham: On Cheese, Civilization, North Country Ballads, &c." in Blackwood's Edinburgh Magazine, Vol. X., August—December, 1821.

The lyrics are on page 443 (Click the link.); the tune is on 446.

The text is identical to that posted by MuddleC above.