The pictures are not the greatest so it is hard to give a good critique. Overall, I don't see any glaring huge issues.
The only thing that seems "off" to me are that his lower hind leg seems to be set under him, instead of straight. The hind legs are also slightly cow-hocked-looking.
I don't see anything wrong with his ribcage depth.
On a side note, I'd caution you against riding barefoot in a saddle. It's very easy for a foot to slip all the way through a stirrup. The heel on a riding boot has its purpose. If you are going to ride barefoot, then don't use the stirrups.
Not a bad looking horse at all!