I have been off the web for a few days, so I've just found this thread.

Malcolm seems to be essentially right about this one, though it might be worth pointing out that the song is (historically) more usually known as "The Lamenting Maid". All except one of the Bodleian copies appear to come from the period between 1813 and 1844. However, this one is, typographically, rather earlier (I'd say about 1800 at the latest).

Bruce Olson links the song (or at least one with the same name) with a number of others in his entry for "Winter it is past".

Ebsworth printed an eighteenth century copy entitled "The Lovesick Maid" in Roxburghe Ballads, VI, p. 240, and noted another copy in The London Rake's Garland (NLS, Lauriston Castle Collection). Two other eighteen century copies have been more recently printed by Hollowell and Black in Later English Broadside Ballads, (I) p. 127, as "The Irish Lovers," and p. 152, "The Lamenting maid."

There is also a useful entry on this useful site, which gives a date of 1787 for a song with this name, probably the correct one as it includes a reply (most of the broadside versions also do). I'll quote it in full.

Six excellent new songs. I. The minister's daughter of bonny Dundee. II. The lamenting maid. III. His answer. IV. An old song to the highland tune. V. A new song for the new year. VI. The north country lass. [Edinburgh]. Printed in the year, 1787 8p.: ill.; 120. National Library of Scotland Lauriston Collection 2901.C.(8). Place of printing suggested by Nat. Lib. of Scot. REFERENCE: ESTCT174346.

Though it claims here to be a new song, this may be worth taking with something of a pinch of salt, as it was a stock phrase of broadside and garland publishers.

Just to add a little spice, you may like to compare the version above with a copy of "The Forsaken Lover" in The Bodleian. This, perhaps, provides a link with another group of songs ...

Hope this is of some help.

Cheers!
Ian