When we put in our arena, it was originally not fenced; after several months, we had one installed. I’ve always started my horses, and had a couple youngsters coming up, so I wanted the physical/visual barrier.
In this area, a lot of arenas are constructed of pipe, which is pretty much what I’d ridden in when boarding or hauling-in for lessons, but I wanted something a little more forgiving if a greenie clipped the fence, or in case one of my legs got rubbed against the fence, or some other such incident. One of my trainers hit a knee on a pipe post at a barn where I boarded, and that really hurts!
So I went with cedar posts and two boards, spaced so that my usual foot/stirrup iron height on the general height range of horses I ride would hit a board, instead of between boards, and reduce the possibility of my catching a toe on a post. Boards are on the inside, posts on the outside, so my knees can’t hit a post. Never have been shoved into the fence, but I’m still happy we went this route. My fence has held up well, with a few of the boards being replaced over the years; I re-stain it every few to several years, so there is some maintenance.
I once audited a non-dressage clinic in which one particularly incorrigible horse ran backwards with such force that he broke a board of the wooden arena fence! Fortunately, both he and his rider were uninjured. But I guess breaking a board is always a possibility; I’d just rather take my chances with breaking a board, rather than my kneecap.
I have also seen fences of portable pipe panels with t-posts and of electric tape with step-in posts. Sometimes, pipe arenas have mesh fencing below the top rail, instead of secondary rails, and one place I used to ride only had the top rail, period – which I didn’t care for.
Really think about where you want your gates – I have a wide gate at one end for equipment entry, and a smaller walk gate at the other end, closer to the paddock (which is the one that gets far more use).