Bought a rescue horse that was almost hairless because of this. Yes, your horse should be stabled in a dry area. That is why they call it Rain Rot also. My Vet told me that it is caused by a bacteria and is not a fungal problem. So your Vet will give you antibiotics for it. I also found out if you buy a ton of those human antibacterial creams it helps get rid of those nasty crusty patches and helps kill the germs also.
It takes a while but it will go away. Plus do not use your brushes on other horses as they could get it too. Hope this helps you.
Your horse should be stabled in dry conditions. The infection is responsive to a course of antibiotics, so you should ask to your vet for the antibiotics!
Talk to your vet about doing a few days of dexamethazone. I have had it recommended by multiple vets in the past when dealing with. I've been told the inflammatory response can become so strong that they have (and I now have) seen horses fully recover with only the steroids because the skin get the chance to heal. I'm not saying you should do that but it would be worth a talk with you vet as an additional treatment.