Logsdon doesn't reproduce the song. Ohrlin's book, from which I took the song, is part of the same Univ. Illinois series, Music In American Life. This series also includes John I. White's Git Along, Little Dogies. Both Ohrlin's and White's books included floppy vinyl recordings, but The Cowboy's Christmas Ball is not among the cuts.
In an appendix, Ohrlin says Chittenden was born in Montclair, NJ, but owned a ranch near Anson, Texas (mentioned in the song), for a while. Ohrlin does not say where the music he includes with the lyrics came from.
Lomax (Cowboy Songs,1910, not seen), in the 1934 revision, says that the song, "slightly changed, was set to music by the cowboys." This probably is the source for Logsdon's statement.