I learned the parody from my mom, who said she sang it in the thirties and forties. Slightly different words:

In the blue ridge mountains of Virginia
Stood a cow on a rail road track
Now her eyes were blue, and oh, so fine
But you can't expect a cow to read a railroad sign
So, she stood in the middle of the railroad track
Along came a train and bumped her in the back
Now her bones are strewn in old Virginia
And her tail's on her lonesome spine.

Ah, silliness!