Punishment & mouthy/biting horses
Why do you think your horses bite? What leads up to it? What are you doing when it happens? What other 'bad' behaviour do they show you? If you've been consistent with the consequences you have described, why do you think they still do it? I think it's important to work out why a horse is doing something before deciding how to handle it, if at all possible. The most effective 'treatment' will be different depending on the cause. The 'bad' behaviour is often just a symptom of a bigger problem.
Eg. You have done something unpleasant, hurtful, disrespectful(in the horse's view) and so he gives you an unpleasant consequence(bites) to try to stop you doing it. So you give him an unpleasant consequence in return, that also happens to be scary. Do you thing this helps treat the real problem? Do you think this enhances the horse's relationship with you? His trust & respect for you?
I don't believe hitting a horse on the face leads to headshyness any more than hitting it on the rump will make it 'rumpshy'. However, the principles of punishment in general are often not well used or understood by the human, who then dishes it out badly & makes it more incomprehensible to the horse, who then becomes 'shy'.
The same applies whether it's physical or 'emotional' punishment. I don't think it's any fairer to frighten a horse out of it's wits than to smack it. In fact I think it's often far more detrimental. Also, if you want to 'talk' a language the horse is familiar with, you often see horses physically punishing each other, but how often do you see them terrifying each other? As you have said, they are very sensitive. I think they're far more emotionally sensitive than physically. Just look at all the uncomfortable & often hurtful things they put up with.
I believe punishment certainly has it's place, but I think it's a very small one and should only be used judiciously with full understanding of the learning principles involved. In most situations it would be far better to use other alternatives to modify the behaviour.
I think you've hit one major nail on the head when you mention timing. People often mete out punishment (or reinforcement) *after* the behaviour has happened. This is a big part of the problem, as it needs to happen *during* the undesirable behaviour and cease when that behaviour ceases to maximise understanding & effectiveness and minimise 'side effects'. Even used with perfect timing, it can weaken the behaviour, making it less likely for the animal to do it again *in front of you* but it can't prevent it from happening.
As someone who has more than a passing association with behavioural psychology, that '3 Seconds' thing really irritates me. Not only does it not take the whole situation into account (any biting, kicking, whatever = '3 Seconds of Death') but it is advocating punishment after the event as an appropriate rule, skewing the message that originally came from behavioural science. That is, the outside margin that horses can potentially link a punishment (or reinforcement) to a behaviour is up to 3 seconds from the behaviour. That means that if you're tardy with your timing, you still need to give the feedback within 3 seconds of the behaviour, worse case scenario, if you're going to bother at all.