When a group of horses live in wide-open spaces and have a home range in the order of 30-80 mi², they are not particularly territorial or at all territorial. If a herd is within this space and another herd enters it all that happens is that they avoid each other and go about their business as before. There is enough room to share. There is no need to defend their territory.
However, if the amount of space available to them is restricted then you might see true territorial defence. If a group of horses meet another group under these circumstances a battle may take place between rival leaders. This is usually the dominant stallions.
The resident stallion almost invariably wins and drives away the intruder and the group. But the winning stallion does not persecute and go out of their way to harm the intruder. All they want to do is to repel them. Once they go, piece returns.
It can be a different matter when horses are confined to stables. The first point to make is that when a horse is introduced to a new stable, they “walk the fence” which means they walk around the boundary of their space to inspect it and as a form of territorial patrol. It tells them about the shape and scope of their space. They then settle down to enjoy the space quietly. But it is much smaller than they would normally have in the wild.
In the wild they may travel 16 miles a day and as a group walk in single file along well-worn paths which they know well.
When they are confined to a drastically restricted space, they can give up their territorial attitudes. They switch off their emotions and accept the cramped space.
But some horses may reject the tiny space allocated to them and become defensive in their small paddocks.
And if a newcomer is introduced to the paddock they may lash out with pent-up territorial aggression.
Under these circumstances it would seem essential that the horse is supervised because the resident horse may want to harm the incoming horse rather than simply drive them off, in comparison to the above. The resident horse may harbour a grudge about the way they’ve been treated or because they desperately need a bigger territory and lash out in an emotional way.
This behaviour would be a reflection of the abnormal spatial conditions under which domesticated horses have to live. A docile horse may become aggressive, a reflection of the fact that they are complex social beings.
By way of contrast, the humble domestic cat is a territorial creature at heart although this innate attitude can almost be removed from their mind because of domestication in multi-cat homes where they too have massively restricted space.