The floater about the tree in the ocean, Ranch Dance website, doesn't appear in the Lomax volumes, nor in Thorp (1921).
According to Silber. "Songs of the Great American West," the version sung by Jess Morris (Library of Congress Record AAFS L2 8) had these lines, which appear in the Ranch Dance version:
'Old Paint had a colt down on the Rio Grande,
And the colt couldn't pace, and they named it Cheyenne.'

Both the above lines and 'The Tree in the Ocean' verse are included in Library of Congress # 5588, recorded by John A. Lomax ("Fife and Fife, "Cowboy and Western Songs," No. 83, Old Paint, text B). This also is the only version I know in which 'Old Paint' is "she." This is the version whose lyrics are recorded in the Ranch Dance site. I have not heard the Morris recording, but I assume it is the same.