Shoe the Colt is very similar to Pitty Patty Polt...

Shoe the Colt - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image

Notes

Here's a similar rhyme from the same book:

Shoe the Horse and Shoe the Mare

Shoe the horse, and shoe the mare,
But let the little colt go bare.

Here's a slightly different version from The Real Mother Goose (1916):

Shoe the colt,
Shoe the colt,
Shoe the wild mare;
Here a nail,
There a nail,
Yet she goes bare.

Thanks and Acknowledgements

These rhymes can be found in The Only True Mother Goose Melodies (c. 1843), as can the illustration. Shoe the Colt can also be found in The Nursery Rhymes of England (1843) by James Orchard Halliwell.