Smacking him in the face would have been punishment. What you did was NOT punishment, it was him learning to respect you as his leader...or you making it hard to do the wrong thing and easy to do the right thing. There's more than one way to do that but it worked, so I'd say you did the right thing!
It seems that you don't understand what punishment is. As far as behavioural effect and what you'd call it, there is no difference between smacking a horse in the face or 'popping' him on the chin or 'kicking like a mare'. Or for that matter, making the horse 'work' when he does 'wrong'. Don't get why you call one punishment & not the others? The term 'respect' and 'dominance' & the attitudes about 'getting it' are very subjective too.
So for future reference...
Positive punishment(+P) is ADDING something UNDESIRABLE('bad' consequence) at the time of a behaviour in order to WEAKEN it. Eg. Any of the consequences OP tried.
Negative Punishment(-P) is TAKING AWAY something DESIRABLE('bad' consequence) at the time of a behaviour in order to weaken it. Eg. Removing food, freedom, etc.
So that's how you weaken unwanted behaviours, and to make wanted behaviours stronger...
Positive Reinforcement(+R) is ADDING something DESIRABLE('good' consequence) at the time of a behaviour in order to STRENGTHEN it. Eg. Treats, a good scratchie, etc.
Negative Reinforcement(-R) is TAKING AWAY something UNDESIRABLE(good consequence) at the time of a behaviour in order to strengthen it. Eg. Removal of pressure, quitting 'work', giving freedom, etc.
Anyway, as OP said, she thinks it's resolved, and also appears to understand that punishment is possibly a temporary 'fix' so she's probably already working with other tactics too, to prevent the 'weakened' behaviour reoccurring.
BTW, I don't just disagree with punishment regardless - I think it has it's place, but I reckon it's important to understand the principles that govern it, so you know when it's appropriate or not and what the 'side effects' are likely to be. I just gave my opinion that I personally wouldn't use punishment in this situation, but would just work on changing his attitude, rather than him just 'copping an attitude' from me.