as in "ride a cock horse to banberry cross..." what is a cock horse? -- (well yes, i know its a broomstick with a "horse head and reins" that children ride... but why a cock horse? I can't remember what we call them-- (a pony stick?)

"Ride a-cock horse to Banbury Cross . . . "
is the correct version, so it is not "a cock (adj) horse," but "a-cock (adv) horse"; i.e, riding with one leg either side of the beast, rather than side-saddle. Which, of course, is the way that you ride the child's toy horse.