I live on a farm in South Africa and around here most horses are kept in camps which are fenced with "normal" wire and usually reinforced with barbed wire. We've had horses on the farm now for the seven years we've lived here. Our horses are born into those camps and learn from their parents how to avoid getting cut up. You will never see their rolling spots near a fence, always in the middle of nowhere away from everything else. However I have seen what barbed wire can do to a horse, when my herd decided they did not like the new Appy mare I had brought in and chased her till she tried to jump the 5 foot barbed wire fence, she was pretty badly cut up. Here in SA we no longer fence with wooden fence posts, especially not if you run cattle, we use metal ones. I will try and post a picture of what happens if a horse runs into one of those. My saddler tore open half his chest on one, what happened, I don't know, having 13 horses means they live out in the veld most of the time. They came down to the water and the workers called me saying Taro has cut his chest open. He was immediately brought down to the stable camp where the wound was thoroughly cleaned and disinfected. The wound was cleaned everyday thereafter. A few days afterwards someone recommended me an ointment only known as "wound magic" some zinc based ointment that you apply every day without cleaning out the previous ointment you put on yesterday. Within a week the wound had halved in size.
So yes, fenccing can and do cause serious harm to horses, but it's what you do about the injury that makes all the difference.