Rope burns usually do not bleed, they "Weep" fluid. They have a tendancy to look healed then when they walk on, it breaks open. They have a real propensity to get infected expecially behind the fetlock. They can get crusty and nasty, in my opinion they can be some of the nastiest wounds.
Just keep up on it, I would clean it every day with an iodine soap and a warm compress to keep it open and weepy, and to keep it from crusting over thus breaking open when he walks. As far as riding , I guess it depends on how deep the burn is. Just be careful with it, they are nasty!