Our internal fencing is mostly visible electrified polybraid, the perimeter fencing is barbed wire, as this is a cattle property and that's how it came.
made the excellent point that the space horses have in a paddock is very much related to their safety with fencing. In small yards and paddocks, they frequently tangle with fences. In large pastures, 5 acres up, I've only ever seen one fence tangle here in nine years, and that was in polybraid, with a silly horse who kicked at it (and never did it again).
Also, fences are dangerous until the horses know where they are, which they may not work out easily when they're going at speed and it's plain wire fencing - so I always run broad white tape as the top strand of plain wire electric fences, so the horses can see it clearly. On the perimeter barbed wire fencing, we used outriggers that run a broad white electrified tape about 1.5 feet inside the fenceline, to keep the horses' legs away from the stuff. If there are horses on the other side of a fence with a neighbour, I erect a polybraid fence about 6 feet from the barbed wire fence, to keep the horses from tangling with each other and the fence.
We also plant shelter belts alongside fencelines, to provide an additional visual cue.
I'd never build horse-specific enclosures from the stuff, and especially small constructions. But, on large pastures with plenty of room, with an electrified tape running on outriggers to keep horses away from the barbed wire, and no horses across fences from each other, you'd have to be really unlucky to have a problem.
Here's an example from the Internet, but ours are spaced wider and use broad white electric tape:
Our internal polybraid in the 5-acre paddocks:
Two new horses a few years ago having no problems at all working out the boundaries:
Electrified white tape on top of "invisible" plain wire electric fence:
A parrot perching on such tape:
Barbed wire perimeter fence with electrified white tape well inside it on outriggers:
Why we have them:
Cattle will break through polybraid occasionally (when there's a fence fault), but not generally through barbed wire. Having a cow in the wrong paddock is an easier fix than having a cow outside your property, on a road etc.