If both front feet are bleeding from the frogs and there is no sign of trauma, I would suspect an advanced case of thrush. I don't usually see bleeding in cases of abscesses
, although nothing is impossible in horses! Hoof abscesses usually travel from the sole up to the coronary band or heels and then break open there to express pus. However, if you have a serious case of thrush, it can penetrate deep into the inner layers of the foot and lead to a deep infection or abscess. The cardinal signs I see with abscesses are severe lameness, heat in the foot and increased digital pulses (These can be felt on either side of the fetlock. You can compare the pulses on the front feet with those of the hind feet. In normal feet the pulses are difficult to feel.) I rarely see abscesses in multiple feet at the same time, but often see horses with thrush in multiple feet.
If you have never dealt with thrush before, here is some information: it is a bacterial infection that thrives in areas of low oxygen, such as around the frog. Unfortunately a little bit of thrush around the frog can be self perpetuating as the more the thrush takes hold, the deeper the penetration into the foot, and hence less oxygen and an even better place for thrush to live. If you've never had a horse with thrush, the main sign of the infection is a black, smelly discharge that starts on the sides of the frog and may extend into the body of the frog and potentially up between the heels. You may have to put your face quite close to the foot to smell the thrush if the infection is mild, but severe infections can be smelled across the room. If the problem is indeed thrush, the remedy is to keep the feet as dry as possible, which means out of mud, and out of water from frequent bathing, and then to apply a product that will kill the bacteria. Many of these products contain copper naphthenate (such as Kopertox), or turpentine (we often use Keratex liquid) which will slow the infection and help to dry up the feet. Sometimes iodine will help to dry up the foot, but often we have to move to a commercial product. These treatments need to be reapplied on a regular basis following the directions on the bottle. If there are open bleeding wounds on the feet I would wrap them as you have described after treating. It is also important to keep up with foot cleaning and trimming as loose frog and poor trimming can help the thrush to persist.
There are other causes of bleeding in the feet, so it is important to check for any foreign bodies that may have cut or punctured the frog, and to have your farrier or veterinarian examine the feet to make sure you aren't dealing with something more serious that thrush. Without seeing the feet in person it is difficult to diagnose for sure.