A cock-horse is anything a kid rides on and pretends is a horse. It can be someone's lap, a rocking horse or a wooden stick with a wooden horses head…

Ride a Cock-horse to Shrewsbury Cross - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image

Notes

Here's another version of this rhyme from The Mother Goose; Containing All The Melodies The Old Lady Ever Wrote, edited By Dame Goslin (1850):

Ride a Cock-horse to Coventry-Cross

Ride a cock-horse to Coventry-cross
To see what Emma can buy;
A penny white cake I'll buy for her sake
And a twopenny tart or a pie.

Here's the version from The Nursery Rhymes of England, 2nd edition (1843), by James Orchard Halliwell:

Ride a Cock-horse to Banbury-Cross

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.

This rhyme is similar to another rhyme called Ride a Cock-horse to Banbury Cross.

Thanks and Acknowledgements

This rhyme can be found in The Little Mother Goose (1912), illustrated by Jessie Willcox Smith. The illustration comes from Kate Greenaway's Mother Goose (1881).