Wireless wunk
There's actually a niche type of competition based on exactly this! It's called "shankless showmanship", "shank" here being a word for the type of lead you normally use in showmanship competition. Here's an example on YouTube:
The horses still wear halters (not bridles) as for safety reasons they're kept on a lead right up until entering the arena. You'll also notice there's only one horse in the arena and they closed the gate after the competing team entered, which is another safety measure. But the handler has nothing in her hands - she's entirely controlling the horse off of hand and body position through this entire sequence. Touching the horse or its halter in any way would be immediate disqualification.
The main challenge of training a horse to do this is for the human to be completely consistent with their body language over a long period of time. The same position has to mean the same thing every time, AND you cannot take that position when you do not want the horse to perform that maneuver. If you're consistent, the horse will learn with almost no further reinforcement. Some horses are more distractible and you might need to use treats at first to keep their attention, but that's all it really takes!
Because horses are herd animals and have been domesticated for thousands of years to cooperate with humans, they're extremely attuned to the body language of their handlers. Moving Together is what herd animals do, and horses have had that instinct fine-tuned in the same way sheepdogs have. Even generally untrained horses will frequently follow a human around if there are no other humans or horses nearby, because their instincts tell them that there is safety in numbers and their domestication tells them that humans are friend-shaped.
The horse in the first video didn't "realize" there was no lead, it got distracted by the presence of Other Human and was looking to the camera person to see what they were doing. Some horses will test and realize that they're not on a lead, but that looks different. This one was just like "Wait, which human should I be paying attention to?" The camera person was also probably someone the horse already knew, which makes them more distracting to the horse than a strange judge at a competition.
Horses have a similar range of intelligence to dogs, and many of them LOVE to Have A Job the same way many working dog breeds do. They'll even start chewing and generally behaving in destructive ways just like bored working breed dogs. This kind of challenge is exactly the kind of task that many horses love!
