I've been looking for a printed reference since I first posted back in 2005. Finally - after years of searching - I found one.
The reference is in a children's songbook called "A Ring Around the Moon" by Edith Fowke. Pg. 35.
The book was published by NC Press - the copy I bought is a Second Edition (1987). The first edition was printed in 1977 - but I don't know if the song is in it.
Here are the words in the book:
The Horse Named Napoleon
I once had a horse and his name was Napoleon;
Named on account of his bony parts.
Bought him from an old Post Indian
Known to everyone in these parts.
He was so thin you could see right through him,
Hair was as soft as the finest silk.
Hitched him to an old milk wagon,
Taught him to stop when I yelled "Milk!"
Along came a dude in the finest livery,
Said to me, "Son, would you run a race?"
Sure as a sinner I was coming in a winner
When the dude yelled "Milk!" and I lost that race.
My mom was thrilled when I mentioned it to her. Yes, this is likely a regionalization of the song - since its not the one she learned, or that many here have learned. Apparently the version in the book came from Kingston, Ontario in the 1940s.