Here is my take. My Uncle sang this while bouncing a younger family member on his knee. The further into the song he was, the faster he sang and the faster he bounced. I have no clue as to where this came from.

I had an old horse and I called him Napoleon
Just cus of all of his bony parts.
He was sired by Old Hamiltonian,
Dammed by near everyone 'round these parts.

He was so fine you could see right through him,
Hair as fine as any silk,
I hitched him up to an old milk wagon
Taught him to halt when I hollered "Milk!"

The other day when I was a-riding,
Along came a man with a rig so neat.
He said, ??????????????????????
I'll run you a race right down this street."

So off we went a helter-skelter,
And I had smile all over my face.
Sure as I's sinner, I's comin' in a winner
When the rube hollered "milk" and I lost my race.