I too was sung this by my Grandpa, and my dad...and I sang it to all of my kids. Our version went like this: (the reference to the "sugar place" perhaps reflects our Vermont roots, for those of you not from New England, a sugar place is a stand of maple trees which are tapped in the spring to make maple syrup.)

I had a horse and his name was Napolean
He had hair of the finest silk
Hitched him to an old board wagon
Learned him to whoa when I hollered milk

I met a man and his name was Bailey
He had a horse and the horse was bay
Bailey said lets have a race
up and down the sugar place

We started out a hilter skilter
Up and down the sugar place
Sure as I'm a sinner I was comin' in the winner
When a woman hollered "milk!" and I lost the race.

(The child is bounced on the knees and let slip between the open knees on the final milk. It has never failed to get a gleeful laugh from any child!)