"A Roundup Lullaby," music by Gertrude Ross, states the words are by Badger Clark. The abbreviated lyrics and and new last verse put the lie to that.
No one claimed the words and music with chords by Katie Lee, given above, are by Clark; they are anon., possibly by Bob Nolan. As noted by Verde Picker, all the words should be sung; Katie Lee gives the full Clark poem on pp. 79-80 of her book.