COCK-HORSE
Earliest quotations in print, from Oxford English Dictionary.
Definition and comments: "It is not clear whether 'cock-horse' was originally the name of a plaything, as it appears to have been by 1577, or whether the phrase 'on (a)cock-horse merely meant in a position (as e. g. on the knee) which was likened to that of being on horseback."

"A. sb. 1. orig. Apparently a nursery term, applied to anything a child rides astride on, as a stick with a horse's head, a hobby-horse, any one's leg or knee."
1540-1 Elyot, "Image Gov." The dotying pleasure to see my littell soonne ride on a cokhorse.
1577 Harrison "England" iii... We oft exchange our finest cloth, corne, tin and woolies for halfe penis* cockhorses for children." *half-penny
1621 Burton "Anat. Mel." Sometimes he would ride a cockhorse with his children.
...2. mounted (as on a horse), astride.
1564-78 Bulleyn "Dial. agst. Pest." (1888) The Drake with all the water foules did stoupe lowe and receive their carriage, and when they were all a cockehorse together they wente into the water.
1584 R. Scot "Discov. Witcher...." They passe...so far in so little a space on cock-horse (on broomsticks).

In "The Oxford Nursery Rhyme Book," Iona and Peter Opie, section on Knee Rides, p. 13: (No. CCV in Halliwell, 1846)

Ride a cock-horse to Banbury Cross,
To buy little Johnny a galloping horse;
It trots behind and it ambles before,
And Johnny shall ride till he can ride no more

p. 40: A version given previously:
Ride ..., To see a fine lady upon a white horse; Rings on her fingers ...

S. Baring-Gould, 1895, "A Book of Nursery Songs and Rhymes," Nursery Jingle XXXIII:
Ride a cock horse
To Banbury Cross,
To see an old woman
Upon a grey horse,
With rings on her fingers and bells on her toes,
And she shall make music wherever she goes.

Jingle XXXIV: (CCIV in Halliwell, 1846)
Ride a cock horse
To Banbury Cross,
To see what Tommy can buy.
A white penny loaf,
A white penny cake,
And a twopenny apple pie.

In a 1901 Mother Goose:
To see an old lady upon a white horse ...
Also in Halliwell, 1853, "Nursery Rhymes and Nursery Tales of England."

To see a Fyne lady ride on a white horse ...

The first appearance was in Gammer Garton's Garland, 1784. I haven't checked the original, but it seems to be:
Ride a cock-horse to Banbury Cross,
To see a fine lady upon a white horse;
Rings on her fingers and bells on her toes,
And she shall have music wherever she goes.
(not in 1810 Garland)