I had (in the 60s or 70s) a collection of horse stories. One was about a Native American young man named (I believe) Johnny, who was a handsome man who was “lame” (walked with a limp and was self conscious about it). He had a horse he named Bay-ee because the horse was sort of copper-colored like a penny. He won some sort of race with the horse. Would love to find this story again.
“Ba-ee” by Kathryn Cook, one of the short stories found in: ‘Horse Stories’ edited by David Thomas, pub. 1964 Pocket Books. The same book was also published under the title ‘Teen-Age Horse Stories”
This book was originally published as Teen-Age Horse Stories in 1950 by Grosset & Dunlap. Editor is David Thomas. There was a later paperback edition titled Horse Stories published by Lantern Press with the same contents. There may have been other editions as well. The story itself is called Ba-ee by Kathryn Cook, and as you remember, involves a lame Native American boy and the orphan colt he raises. The book is freely available in both paperback and hardcover on the used book sites, and not expensive. I’ve owned a paperback edition for decades.