I wonder if this is the one CapriUni knows, too?

Nope. The song that I learned only had the lines:

"The old grey mare, she ain't what she used to be
ain't what she used to be
ain't what she used to be
The old grey mare, she ain't what she used to be
39 years ago."

And the tune had more of the same feel as Camptown Races (though that's not the same tune, either)

This tune (playing now) reminds me more of "Buffalo Gals" ... Like I said, like describing a flavor...

I suspect we may be talking about different songs with some lines in common.

I think I'll try a Google search, and see if I come across something that rings a bell.

Be back later...