It would seem like a viable fencing barrier, but I have a few negatives. (I have used the fencing for paddocks with a top strand of electric to keep horses off it.) For safety sake I think you would need a top board and a bottom board and maybe even a middle board!! The wire is twisted and the edges are quite sharp. If a horse or ejected rider were to get slammed into it the result would be some serious cuts and abrasions. I think if I were using it I would build a three board fence on the inside of the posts and put the wire on the outside of the posts. Sounds pricey, but i don't think I'd like to be riding a silly horse with only the wire as a boundary. JMO.
The no climb fencing we have used is welded so maybe I am calling it by the wrong name. It is pretty smooth not pokey. My plan was to use only a top board as an added visual but honestly I would rather bounce of the woven wire than hit a wooden fence. Hopefully, bouncing, falling, ricocheting, etc. won't be a common occurance. We try and just keep the old steady retirees at our place.
If it isn't woven,it is not technically "no climb" but just 2x4 welded wire. Softer landing!! Make sure you install it so the horizontal wires are on the outside of the riding area. The welds break easily when hit by a hoof. Good luck.