That's a simple answer.

No.

It wasn't until the 1920s that most areas required even auto licensing.

You didn't need an operator's license for horses, mules, donkeys, oxen, dogs, goats, or anything else drawing a vehicle. In fact, driver's licenses took awhile to catch on. No one was going to test your ability to drive when there were so many kinds of cars, no standardization of equipment, and - here's the kicker - no street marking or signage like we know, and no established parking spaces.

With horses - what purpose would it serve? You can't attach an easily visible number anywhere without damaging the horse, that it won't be easily covered by a choice of harness or tack, or easily removable or changeable. No, don't say brands. They aren't that visible from that far, and then only from certain directions. Lots of harness pieces might obscure them, as would a fly net.

License plates certify that a car is in minimally safe condition (safety inspection stickers), paid up on its taxes, and allow it to be identified when speeding away or parked improperly. Horses were never certified for soundness, and there are books that will include those dealer's tricks for covering problems. Horses were not taxed that I ever ran into, though taxes on portable property is something I have never looked into.

It's hard to prove a negative, and someone may pop in with the regulations of Lower Treesquat as registering horses in 1879, requiring a whitewash code on their rump. I will simply point you to the carriage and harness and tack section of any period Sears catalog. They do not sell license brackets for carriages and wagons, nor anything for holding a license on a horse. They sell nothing for making license brands more visible.

I would positively look forward to finding out I am wrong. It would be a hoot.

Hi! I wrote an answer to a similar question that you might find helpful: Were horses licensed like cars?