Wood plank fence.

This looks like a very sturdy wood fence, suitably tall for the horse kept inside.

The bottom plank is close enough to the ground to prevent pushing under, yet not too close so that a hoof is unlikely to get caught under.

It would be somewhat safer to mount the boards on the inside of the posts, so that the posts themselves do not become a hazard, and so that if horses are pushing on the planks, they are less likely to push the planks out of the posts if the nails are not secured well enough.