A blanket can be good or bad. One one hand, it does keep the moisture off them. However, they cut a lot of the air flow off the coat and so the bacteria can fester under the blanket. If I were you I would avoid keeping blankets on for extended periods of time unless it is raining hard or it is cold. Just try to keep the horse out of any deep, wet areas of footing. The more you can clean the paddock/stall and keep it free of manure and urine, the better. I worked with a horse that had rain rot for over a year on a hind leg and currying it every day twice a day worked wonders, so I would recommend currying. The curry comb basically loosens all the dirt and hair, so the bacteria doesn't have as much as a chance to grab on and soak in to the skin. And like others have said, avoid sharing brushes.
If your paddocks get really mucky during the winter, I would advise keeping the horses in fresh clean stalls or shelters until the paddock isn't as mucky.