I am sure had I been that carriage driver, my response to those obnoxious twits would have been the same. If you want to be listened to and regarded with respect then you can treat people with that same respect.
Those drivers are making a CHOICES to make a living but are not required to put up with that kind of crap for sure. They are not public servants not sitting in elected positions so I don’t think the comment about being in the public eye is really fair - unless you consider that you should be able to walk about and be rude and harass anyone at all out in public and not expect some negative reaction to it.
These women butted their noses in in a way that was counter productive. They did not care about the welfare of the horse so much as getting themselves some publicity on youtube. If they had really cared about the horse, they would not have played it up for their camera but would have quietly waited for the driver to come back and asked him about the horse in a nice way at that time.