We've always kept our horses in wire, electric and barb, except for our sacrafice paddock which was wood for awhile. I recently changed it over to electrified white tape/rope.
Our Walkers were kept in without incident for 15 years or so in a single strand of barbwire. The only time we had a barb wire problem was when they dug up the previous owner's wire in the paddock unbeknownst to us. One of our mares got it wrapped around her leg, but it healed up quickly and without major injury.
As W_S said there are some very important factors with any type of fencing and wire in particular.
1. Space. Horses need a decent amount of space. My sacrifice paddock is 3/4 of an acre. I have 2 horses in it. I would only put another horse in there IF it was a correct personality type. Horses need to be able to get away from each other without going through the fence. Our pasture is about 2 acres and was fenced in barb wire. The sacrifice paddock was wood when we had 3 horses, now it's 2 strand electric rope and I have 2 horses in it.
2. Food. Do the horses have enough food? If they don't, you're asking for them to test the fence.
3. Herd dynamics and stability. If you have a very stable herd with non-aggressive horses you can more easily keep them in "lighter" fencing. If you have any aggressive horses or changing dynamics (young/new horse figuring out it's place) you either need a lot more space or you need heavier duty fencing.
Others made valid points too, sight lines, fencing shape, shared fences, etc are all extremely important with ANY type of fencing.