Don't know who is responsible for the first verse, but the one about the horse was collected by Perrow in 1909 in trad. and also traces bach to the early minstrels.

Old Gray Horse (and other names), "Clare de Kitchen," "Went to the River," etc.

Went to the river and couldn't get across
Paid five dollars for an old gray horse
...

Wouldn't go erlong and en' e' wouldn't stand still
But jumped up and down like an old fluttermill.

Many verses, many floaters to "Old Gray Horse." Earliest one with that verse and rhythm is "Clare de Kitchen" by Rice (minstrels).