The original writer of "Platonio" has yet to be established beyond question. The most convincing claim argues for Harry C. Aliff, who wrote as Harry C. McAulife, aka. "Big Slim the Lone Cowboy". Somewhere here there's a post from his son, Ken Aliff. He gives the horse's name as "Patanio".

But I have serious doubts, because Harry didn't begin his career until 1929, whereas the earliest known published version ("Plantonio") was collected by Margaret Larkin and appeared in her book Singing Cowboy in 1931. That's a real short time for a song to enter the tradition and evolve into a significantly bowdlerized song. A lot of those early performers claimed to have "written" songs they merely tweaked or arranged from other sources. I would say, however, that Aliff was responsible for its wide dissemination among later performers.