Possibly when standing, NOT at all gaits. Horses are vegetarians and so are prey to carnivores. Their sole defenses are keen eyesight and flight, therefore they are well adapted to see anything that moves such as lions or tigers lurking in the undergrowth. So well adapted are they that this is the reason why the horse has not become extinct many thousands of years ago.

However, this eyesight, attuned to movement is not so accurate when faced by something static such as a fence. The horses' eyes can then only make out objects above about an inch (2,5cm) wide. When the fence is wire the problem is compounded a thousand fold. Even humans have great difficulty in seeing wire and barbed wire fencing from as little as 10 yards (10 meters) away so what chance a moving or panicked horse ?

in that their natural reaction to danger is to butt or kick. Therefore they move more deliberately and so tend not to become entangled in wire and barbed wire fences. However they still get cut by barbed wire which reduces their value. As an example the Rolls Royce Company will only take hides from cattle raised behind electric fencing as they do not wish to have the blemishes of scars.

Because horses panic very easily their movements tend to be violent and unpredictable even to themselves so they cannot easily and quickly distinguish something that is barely visible to them.

Slaughterers estimate that 5-10% of the horses they put down are those that have become inextricably entangled in barbed wire fencing. The cheapness of barbed wire is offset by possibility of very large Vets bill and life long scarring or even the painful death of the horse.

So now you know... Don't take chances with your precious horse.