This is a proverb about taking care of horses. It can be found in print as early as 1639. It's a variation of "Uphill favor me, down the hill beware thee."

Uphill Spare Me - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image

Notes

Here's a variation:

Uphill spare me,
Downhill forebear me,
Plain way, spare me not,
Let me not drink when I am hot.

Here's another version:

Up hill bear me;
Down hill spare me;
On the level spare me not,
But cool me when I'm hot.

Here's another from Traditional Nursery Songs of England with Pictures by Eminent Modern Artists edited by Felix Summerly (1843):

Up The Hill Urge Me Not

Up the hill urge me not,
Down the hill ride me not,
Along the level spare me not,
In the stable forget me not.

Thanks and Acknowledgements

This rhyme and illustration can be found in The Sleeping Beauty Picture Book, illustrated by Walter Crane.