Parallel Anthology Track 7
No image of record label available. Neither Anthology booklet assigns authorship, nor does www.78discography.com.
The Roud Folksong Index classifies this song as a version of Roud 414, and also lists a version collected by Cecil Sharp in 1908.  Perhaps the book which contains this version (English Folk-Songs Southern Appalachians 2) has more information about the origins of this song?
It seems reasonable to treat this composition as public domain, although the evidence for this is not particularly firm as yet.
The Wagoner's Lad by Peggy Seeger album released in 1955: Spotify Liner notes make no claim to copyright for writing or arranging.
The Rose of Naideen by Mrs. Laura McDonald recorded in 1958: Max Hunter Collection
My Horses Ain't Hungry by Mrs. Haden Robinson recorded in 1960: Max Hunter Collection
My Horses Ain't Hungry by Mrs. Kenneth Wright and Mrs. Gladys Jennings recorded in 1960: Max Hunter Collection