The horse
As a species the horse evolved on the vast planes south of the advancing and retracting ice cap during the ice ages. The social behaviour of the horse is based on having virtually unlimited space. Avoidance is the key. Aggression can simply be avoided and even scarce resources like food and water can be dealt with by moving on.
Predators are given a wide birth and even the panic flight does not extend beyond the attack range of a large cat.
The only exception is the tactic against wolves; wolves can outrun a horse thus flight is not an option. The family chooses to form a defensive wall of teeth and hooves around the foals and prove they cán fight. Especially the harem stallions are accomplished street fighters and even these provide solid proof for avoidance as the main survival strategy; serious conflicts between the harem stallions of the different family groups within a large herd are extremely rare. Everybody can always move away or go a bit aside as a compromise. There is no 'back to the wall'. Even against wolves they, unlike other plain dwelling herbivores, choose to fight.
The horse is not a territorial breeder; where the family group is, is their home. Wherever they are on the vast planes.

The popular dominancy model is not correct; not all of it at least. Each horse can simply move away if it not happy with the situation. If living in a specific family group is not worthwhile for the individual horse it can simply move to the neighbours.
A lead mare and harem stallion are therefore those horses that prove to be the best leaders; those that prove to be in the best interest for the individual family member. 'You get what you reward' at its best.

The other face of the same coin is the inherently resulting stress from the lack of the possibility to avoid the pressure. Simply the lack of an 'open door' makes the horse acutely aware there is no way out and it automatically switches to wolf mode; fear aggression, stress.

For me this translates to riding very simply to the 'open door'. Always allow your horse space; physically and mentally.
The horse is a professional claustrophobic; always leave a door open.

A horse seeks food and safety; it wants to survive. The survival strategy of the horse centres around the herd, and the family group within that herd. To enhance its chances an individual horse want to follow the best survivalist; the lead mare, and seek protection of the strongest; the harem stallion. This is where the rider can fulfil the key position.

The rider
Apart from climbing trees the horse is superior to us in just about everything. The rider, the human, only has one real advantage: brainpower.
Using this superior brain the rider can easily avoid, outmanoeuvre, bend, and manipulate to give the horse the impression that he’s dealing with an extraordinarily powerful individual.
Since the rider ís the cleverer one of the two, it should be quite easy to prove to the horse that he is the best survivalist and the one to follow.
The rider holds all the trump cards to be the safe haven; to be the leader to follow and to seek refuge with. The horse will 'flee' towards you.

Under the saddle this translates into a rider who takes the correct decisions and who saves the day in 'dangerous' situation.
This means not being a source of extra stress; not holding back the horse with a tight rein, not grabbing hold of the horse with the legs.
Since the rider obviously does not abandon his mount, obviously will protect is, all you need to do is to let the horse perceive this: you are the safe haven. If nothing else, that is in your own interest!
So, do not pull the reins nor squeeze the legs; that is holding back and spurring on. Both are stress enhancing, and also conflicting signals and thus even more stressing.
You 'let go' and show an 'open door' to a safe exit. That is not saying you need to actually go there; you just give the horse confidence. If there is no escape route, no safe exit to show, then you have made an error in judgement but you still have yourself to bé the safe haven, the best place to flee tó.

The Centaur
The Home Caballus is the synergy between rider and horse. The human brain and the equine body. The rider gains horsepower, the horse gains brainpower. A clear-cut win - win situation.
When you can achieve that the horse sees you as the superior brain, recognises its interest in your multifunctional leadership it will seek that. The horse will wánt what you want.
Then you will share a mutual set of fine communication signals and the result is mutual enjoyment in the mutual undertakings. Unbridled, unreined all you need is a good saddle to prevent your weight to be a burden and you can tackle the world together; horse powered brainpower.