I believe the problem is the bad farrier job covered in this topic.
Even with the exercise pad, I'd only walk him on soft ground, like thick grass and sand. Hopefully his hooves fix quickly, the poor boy. Honestly, though, if the biggest moment at the moment is him being flat, I'd consider some shoes. They worked wonders on my QH to get his frogs up off the ground. By rights I could let him go barefoot now that his hooves are better, but I do a lot of road riding so I've opted to keep the shoes on.