I've ridden in a Barefoot Cherokee, which I had for my old mare who was a Welsh D; also I have ridden in a Barefoot Cheyenne at a friend's yard, but not on any of my own horses.
IME Barefoots don't usually fit well on wider horses and/or with flat withers, where they tend to be unstable. They seem to be best suited to narrower horses with defined withers and good musculature.
Having said that, when I had my little youngster first (tubby little coblet!) I rode her on in a Barefoot, but then a day came when she "told" me quite firmly that she wasn't keen on having it on her back anymore! I'd already got a TreeFree Tor saddle for my other horse at the time, so after a change of gullet, put this on her and it fitted fine!
I also have a solutions smart on a very wide, low withered traditional gypsy cob and itâ€™s the most stable, comfortable saddle Iâ€™ve ever sat in. Doesnâ€™t move an inch in any direction, and no special girthâ€™s or pads needed, dead easy..