Shoes would make it more likely for them to slip and dramatically increase the concussion going to their legs and joints, which if done repeatedly could contribute to arthritis later on. I probably wouldn't do more than a trot if my horse was shod, and not for a long distance.
A barefoot horse on the other hand would have better traction and the hoof would be able to expand and absorb some of the shock, reducing the amount of concussion that reaches the legs and joints. I would be much more comfortable trotting on a barefoot horse, but I still don't know if I would canter.
The horse's condition should also be considered. A more fit horse will have stronger tendons, muscles, and even bones that help it to hold up better. I wouldn't take a horse that wasn't used to it and make him run down a road. But, if your horse is fit, I wouldn't see any harm in doing it occasionally, but it isn't something I would want to do daily.
"Horses don’t have hard mouths, they have hard, stiff bodies. The softer you can get the horse through his body, the softer he will be in your hands." Clinton Anderson