I spoke with a vet about her favorite, or least favorite, kinds of horse fencing. She took me by surprise because she was not totally against barbed wire. Although barbed wire is better for cows with thier tougher skin, she felt like once the horses knew the boundaries, it was not much different than any of the rest. Of course she had some gruesome stories to tell about horses running through brittle vinyl fences in the winter, and electric wire tangled around horses feet.
A friend of mine researched everything when she was deciding on her fence, and ended up with a single board at the top and wire mesh with tight enough weave that hooves could not go through easily. My fence is three-board oak, painted black, and I love it. It is easy to hop over when I need to take a shortcut.