How big is this pasture and how many horses are in it? I have miles of barbed wire and 28 horses very few cuts.
If you do not overcrowd the pasture then I can't understand why your horse is getting cut so often. I insist on at least 2 acres per horse in any pasture that mine are kept in. I ahve never had a serious injury due to barbed wire. If it is well maintained and the pasture not overcrowded your horse should not be getting cut.
Most large ranches here in Texas have barbed wire only and keep all the livestock in using it. IMO it is no worse than any other type fencing if properly maintained. All my foals are born in pastures with barbed wire fencing. They learn at an early age to respect the fence. NONE have any scars from their encounters. Shalom