My father used to sing this song in the car on road trips when we were children. Here are his lyrics...
After the initial refrain...

Now the farmer takes the old gray mare, sits by the side of a thoroughfare, he can make more dough just a waitin there, than he did long years ago.

Well the farmer makes five bucks, for towing in cars & trucks
Yeah, he's the old boy they all call a rube,
they give him a kick, naw, but he's got the boot,
Aw cuz he's not stuck with a flat inner tube,
him or the old gray mare.

Refrain...