Barbed wire is fine if you have a LARGE pasture and horses that aren't accident prone, but it can cause injuries pretty easily if a horse decides to reach through to the other side, or scratch their neck on a post. You can put electric up on existing barbed wire to keep the horses off of it.
If you're putting up a new fence, the cheapest way to go is barbless wire. It's just like barbed wire, but without any barbs on it, hence the name. It's smooth twisted wire. You can use a single strand of electric to keep the horses off of it.
For electric, I have had VERY good luck with Electro-Braid. It's pricey, but SO EASY to install! And it just won't break! I have seen two horses jump right in the middle of it (spooked), tangled all up in it, and pop right back out without a scratch! And the fence snapped back like nothing happened... It was great! That convinced me to use it on our place. We have a very nice existing wood fence and I wanted to keep the horses off of it. It's about an acre pasture. I was able to install the whole thing by myself! I did have my DH put the ground rods in, as our ground is very rocky and a PITA the get through.
The advantage to electro-braid is you only need fence posts every 50 feet, FIFTY FEET!, plus brace posts every 400 feet and at the corners. You'll use 1/3rd the posts you would with wire, wood, or traditional electric (wire or poly tape/rope). The rope is soft, feels like cotton, with copper wires braided in. It's light weight and easy on the hands (if you forget your gloves like I did, lol
.). Electrobraid - Electric Horse Fence, Safe Livestock Fencing