As we originally made the fencing for the dry lot for two full-sized horses, it was treated posts and treated decking lumber. There is 8 feet between the posts. Then the fencing was stained white opaque with a water-seal stain to help preserve it. We have electric wire at the top of the top rail, which was to stop cribbing. We have an electric tape between the bottom rail and the middle rail. That was mainly to keep the minis from sticking their heds over and chewing the grass all the while, and to keep dogs or kids from climbing in. Has worked for both. It is probably overkill for minis, but it will withstand any kicking and maybe would slow down a predator from coming in over the fence from the outside. Since we aren't home during the days and are not right next to the barn at night, I wanted something sturdy for them to stay in. Have had no issues.
Had I started with minis, may have been different, but even with minis only, we are keeping big horse dimensions so any possible change in plans or owners will keep it flexible.