One strand of fence works just fine as long as it is always on...you just can't leave it off for long periods, and you have to stay on top of making sure it's not down someplace.
We had one strand of hot wire for years just nailed to trees. It wasn't till I got lazy about keeping it hot that we got into trouble. One horse figured out he could go thru it and then even when it was hot we couldn't keep him in. That's when we got good fencing around the perimeter. I still just use one strand to divide the property inside the perimeter.
Becky
I think Bay would stay in it... I don't know about Cyn, but I think our pony would go over it or under it if there was just one wire. She's done that here, when I had a temp fence up for something or another.