For the last 15 or so years we've had a single strand of barb wire enclosing the pasture. The paddock started out barb wire, changed to 3 board oak, and is now a single strand of electric wire. I just changed the pasture to 2 strands electric rope.
The only problem we ever had with the barb wire was one of our mares would crawl UNDER it if you took the gelding out without it.
But we've been lucky because our horses have never been fence testers or busters. Well, except last spring when there was something wrong with the wire and there was no grass and they were both on diets... the grass was definitely greener on the other side then!