Here in Australia it is the most common type of fencing that horses are kept in - Normally they are kept in paddocks originally made for sheep or cattle.
I have my horses behind wire all the time. They have been in plain wire, plain wire with sighter wire on the top strand, wire with a stand off hot wire, and at the moment, plain wire with a strand of barb on top.
I've only had maybe one or two fence injuries in the 10+ years i've had horses in these fences, and both were due to extenuating circumstances (Mainly other horses getting loose and into the adjoining paddocks).
I am well aware that wire isn't the safest fencing for horses - However it doesn't have to be the horror story many people think it is.
I think the main things that make wire fencing safer are:
The horses need space within the paddock to run around, play, spook, etc. without risking running into the fences. I would really avoid using tiny paddocks that have wire fences as in the smaller spaces, especially if there is a dominant horse, they can get pushed into the fences with no way to escape. A decent amount of space means they don't run that risk.
This is an obvious one. The shape of the paddock needs to facilitate movement - So no narrow parts heading into corners, etc. The same reasons as above - So they can't be caught in against the fence.
The best way to keep wire fencing safe is to NOT have other horses on the other side of it. Playing over the fence, fighting over the fence - These are the easiest way to get a horse injured in a fence.
The fence needs to be TIGHT. Loose wire wraps and tangles. Our fences are always secured with metal star pickets with wooden stay posts cemented in every now and then (These stay posts are at least six inches wide). Wire fences need to be kept well tensioned, and it is impossible to do with sub-standard posts.
I guess I just wanted to dispel some untruth's out there about wire fences. If you manage it right, it is no more dangerous than any other type of fencing.