I know of no reason to believe that this had any folk existence before Hirsch and Kaplan wrote it. But it seems to have had variations after.

A few heterodoxical verses cited by DT contributors and elsewhere on the web seem to show the song has taken on a life of its own. For example:

Horsey keep your tail up,
Let your feet go clippety clop

All the horsies in the zoo
Keep their tails up, why don't you

If you want to be real smart
Raise your tail before you [fart]

Does anyone know of any other "Horsey Keep Your Tail Up" lyrics (apart from Childre's, of course) that parody or otherwise differ from the Hirsch/Kaplan song?   Bob