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 Wagoner's Lad by Pete Seeger album released in 1957 according to Folkways: Available in BL, shelfmark 1LP0082764: Spotify No claim to authorship or arrangement on liner notes
Pretty Saro by Guy Carawan album released in 1959 (according to www.folkways.si.edu: Spotify Liner notes say "This version from Sharp's English Folk Songs of the Southern Appalachians, Vol. II, page 12, was popularized among city singers first by Elizabeth Harold and Hally Wood."
Pretty Saro by Guy Carawan and Peggy Seeger from 1958 album "America at Play"
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