I do all the time. I don't have a huge pasture to work my horses in, so I take my seasoned ones out on the road and work them. These horses don't spook at dogs, etc., etc. Never had problems with my horses working them on it. They are all on joint supplements to ensure they are in good shape. But I'll walk, trot and extend a trot on the road. I mainly just walk and do a light trot though (but work them on an extended trot for a couple minutes to be sure they got it for show). Like I said, never had problems in all the years I've done it. My horses have never showed any signs of being hurt during or after their workout.
But you have to remember some horses are tender footed naturally. So they just can't work on the road. My horses all have hard feet (kind of like their heads sometimes
). But care for you horse properly and you'll not have problems. If I had a better place to work them, I would. But I don't.