The song goes back to a 19th century broadside. Rev. Baring-Gould had it as "Farewell He", Garland of Country Song, No. XLIII, and references a Catnach stall copy.

It's loosely related to a cluster of songs of which Gus Meade, Country Music Sources, finds an 1889 original as "Lonesome Scenes of Winter."

U.S.:
H.M. Belden, Ballads and Songs Collected by the Missouri Folk-Lore Society, p 492, has a 1906 version as "Adieu to Cold Weather."
E.C. Perrow found a fragment as "Forsaken" in Mississippi, 1909.
Vance Randolph, Ozark Folk Songs Vol 4, 236-41 has a cluster of versions of "Adieu to Dark Weather."

Between 1930 and 1937 "Lonesome Scenes of Winter" was recorded under various titles by Lewis McDaniel and Walter Smith, the Carter Family, Daddy John Love and Odus Maggard and Woodrow Roberts.

The version usually known as "If She's Gone Let Her Go" was found in 1928 in the Ozarks by Vance Randolph as a version of "Adieu to Dark Weather." From this and the Belden version Paul Clayton and Roger Abrahams slightly rewrote it (mostly changing the sex from "he" to "she"), duetted it in Greenwich Village, and it was later recorded by Clayton in the 1960s.

The Catnach version follows.

Bob