Maybe bracket is a poor choice of word. Use another board an inch or whatever away from your upright to create a channel for the pipe to slot, and pin your pipe inside that channel. Sure, add a chain for strength, and use a drop pin through each pipe end, through a chain link, into your “bracket,” to secure the whole thing.
Everything would be inset, nothing sticking out to catch a horse or any gear. Just another board along the wall. And if (when) they rub on it, the wood on either side of the pipe will help support that load, rather than a snap or whatever taking all of it.