I do not think it is a dominance thing. I think it is a horse saying "Don't be mean to me. I'm not going to try to hurt you. I just want to meet you."
I think it is the behavior that replaces 'clacking' in babies. Babies 'clack' up through yearlings and some 2 year olds. [Clacking is the chewing motion while stretching their necks out when a baby is saying "Don't hurt me. I am just a baby."]
When horses greet and bow their necks tightly they are 'posturing'. I do not think you have a 'threat' or 'warning' when ears are up and horses are sniffing instead of bowing up. Horses, especially really broke horses, should never posture under saddle or in hand. They're very tense and not just sniffing when bowed up. The neck that is 'bowed up' is hard as a rock.
It's just a greeting. One horse is learning the other's scent. Like my pony and his friend Caesar in the picture below. Ears are forward and noses touch. The squeal doesn't always happen, but I think it usually comes from the horse that has more tendency to be dominant. I have never heard Joe squeal and he is always near the bottom of the herd - by no means a dominant horse.
We have two mares who don't care for the blowing in the nose thing.But the gelding...he is much more interested in the activity. Blow-sniff-blow-sniff. But what he really is looking for is a beard to scratch his nose on. So far I have disappointed him as far as the beard thing goes.
Sky- Perhaps he is not yet comfortable with the idea of his head being so close to your mouth? (remember, predators eat things with their mouth!) Or maybe he doesn't think that humans *do* that (by that, I mean the breath exchange thing). He may have never considred that he could greet you in this way.