I think it is widely accepted that when two horses ask, “Am I in charge of you or are you in charge of me?”, the one who moves the feet of the other is the more dominant horse.
Horses are an enigma for everybody (even if people don't know it). We can’t possibly know or understand everything that goes on inside their head. We can take a guess and hope we guess right sometimes. But we have no right or basis to claim certainty because we don’t know how much we don’t know.
We all know when horses meet for the first time they decide within moments to be friends or not. They go through the “introduction ritual” then they’ll either gallop off together or, one will chase the other away. I’ve seen it a thousand times.