CWS said,
. . . it might have been "I'm ride'n Old Paint," and it is likely that it was "I'm leading old Dan." This makes sense, and "I lead an old dan" does not.

I believe it's just the other way around: "I ride an old paint" "I lead an old dan" makes sense, but "I'm ridin' old Paint" "I'm leadin' old Dan" does not. It's like my saying, years ago, "I drive an old Beetle and I haul stuff with an ancient International," to put it into a (relatively) modern life setting. To fit it to this tune and get rid of the capitalized trade names,
"Well, I drive a German SEE-dan
Fer when I haul, I got a truck
But I'm driving down to Sady's
To get myself a..."

Ohh, ah. . . Well, I'll just let that go.

Anyway, I didn't drive "old Charlie" and haul with "old Bessie," because those personifications are neither necessary nor appropriate to how the respective vehicles fit into my life.

Now, say if the riding pony in the song were specified as "Charlie", then you might be right about likelihood, because Charlie is definitely a name, but, as has been said at various times in this thread, cowboys riding (or leading) horses were not ordinarily dealing with pets, and a mere descriptive reference, such as "paint" (palomino et. al) and "dan" (dun) here seem to be, would look to be much more likely. And if "paint" and "dan" are mere descriptions or categorizations, they shouldn't be capitalized, any more than "sedan" or "truck" would be.

Dave Oesterreich