Ears aren’t known for “hanging low” or “wobbling to and fro”. Was this song originally about some other body part?
I had heard it was originally “balls” not ears; but I haven’t looked for a citation
When I was a young’un, it was balls. No ears, no other body parts.
Since it would be very hard to throw your ears “over your shoulder like a continental soldier,” you can reckon that the original version said “balls.”
The lyrics.
I’d guess the original was ‘hair’. It can hang low, it can wobble (after a fashion), it can be tied in a knot or tied with a bow. People tended to have long hair in the late-18th Century (at least from illustrations I’ve seen), so it might be thrown over one’s shoulder like a Continental soldier.
My kids sung this in pre-school, so I didn’t think much about it, thinking it was just a silly kids’ song. I didn’t think they’d changed the word “balls” to “ears.” :smack:
I guess since they cleaned up Eeny Meenie Minie Mo, they cleaned up other songs too.
What was dirty about Eeny Meeny Miny Mo?
One version had the line “catch a nigger by the toe”
It originally said “nigger.” Now people say “tiger.”
Dirty, no.
Racially insensitive, yes.
It didn’t used to be a “tiger by the toe.”
And the following line is now " And if he claws you to death, let him go." 
I’ve heard ‘do your tits hand low’, but only recently.
And for the tiger, it’s: If he hollers, let him go.
Back to the OP, the first non-sanitized version I heard was “boobs.”
(I’m glad I haven’t heard Brazil nuts called by their vulgar name for a long, long time.)
I’ve always wondered about this. What would a continental soldier normally throw over his shoulder?
Do your tigers hang low?
Nah, that would never catch on.
I was just listening to this song this evening with my preschooler and thinking how sillly it was … “balls” makes slightly more sense. 
The more sanitized version is “do your boys hang low”.
What? I always thought that song was about a dog.
A rifle, almost certainly. At least that’s how I learned it in first grade… the song had motions to go along with it, I believe.
I think the “ears” version might have originated in a Bugs Bunny cartoon. Bugs, of course, has considerably less difficulty in tossing his ears over his shoulders, or tying them in a knot or bow, than most humans would.