Here's how I sing it, based on 1960's versions no doubt with some folk processing by me. Tune is the Peter Paul and Mary version, I'm pretty sure.

Oh Stewball was a racehorse, and I wish he were mine.
He never drank water, he always drank wine.

His bridle was silver, and the bit it was gold.
And the worth of his saddle has never been told.

So come all you gamblers, whoever you are
and don't put your money on the little gray mare.

Most likely she'll stumble; perhaps she will fall.
But you never will lose boys, on noble Stewball.

Oh the fairgrounds were crowded, and Stewball was there
and the betting was heavy on the bay and the mare.

But a-way up yonder, ahead of them all,
Came a-prancin' and dancin' my noble Stewball.

I bet on the gray mare, and I bet on the bay
I'd a bet on old Stewball, be a rich man today.

But wherever I wander, and wherever I roam,
I'm a poor boy in trouble and a long way from home.
=========
I've been to the horse races two or three times. For me the best part is the sound of the crowd as the horses approach the finish. There is no other sound quite like it.

It is my belief that as for betting on the horses, you might as well bet on Poohsticks for all you can predict. The boy in the song backs this up - he's enamored of Stewball, but it's all hindsight.