If a horse decides to go through an electric fence it doesn't matter if it's 1, 2 or 3 strand. They are much stronger than a fence and will go through, the difference is how much damage they do to themselves in going through it.
Not all areas are suitable for multi strand wiring to keep horses from grazing under the top wire. Where I live, in the spring, grass grows so darn fast you practically have to cut it every day to keep it from grounding out the lower wire. Later in the year there is other grass/weed related issues that mainly impact the lower wire and still a pain to keep from grounding out the wire. We don't get the snow here but that's a major problem for lower wires in snowy areas, 6-8 inches of snow and your fence is grounded out. I'm sure other areas have their own issues with low hot wires.