Sounds like either "rain rot" or ringworm. Both are a fungus. Rain rot is something they get when they are in a constant damp environment, and with their long winter "wool" - they develop a fungus. Generally rain rot spots remain small, like a large pimple, such as you described.
Generally with rain rot, a betadine bath and the TOTALLY drying the skin and hair and keeping them dry for a few days should take care of the worst of it.
Ringworm is a highly contagious fungus that is a circular scab. If left untreated - the circular scab will get bigger and bigger and bigger. It effectively kills the hair folicles, and after you have gotten rid of the ringworm, the hair takes a long time to grow back in. We had this all the time with our dairy calves - and sunshine killed it when they were sent outside in the spring. The worst was in the winter months when the calves were kept inside in close quarters. I also had a horse a number of years ago that I bought that had a case of it.
Treatment needs to be aggressive and done on a daily basis until it is gone. Wear latex gloves and scratch the worst of the scab off -- if it bleeds a little that's OK -- because it allows the medication to get down to the root of the ringworm. I use athletes foot medication for around the eyes because it is a creme and won't run. Betadine on other areas is fine but be careful - it could cause "burning" on sensitive skin. I prefer to use an anti-fungal creme on all areas.
Keep the horse away from all others until it is gone. Bleach the stall and feeders before letting any others use them. And be sure to WASH YOUR HANDS every time you touch that horse!! Believe me, first hand experience here. You don't want to get it yourself!