Be sure you don't confuse 'Ringworm' or 'girth Itch' with 'Rain Rot' -- they are not the same thing. Ringworm and Girth Itch are very serious fungal infections that are extremely contagious and ARE spread by equipment and people. It is not, to my knowledge, affected by Vitamin A levels as is Rain Rot.
If a horse has Rain Rot, it will be mostly confined to the top of the horse -- his back, rump and even the top of his hocks. Most horses get it first and worst on the tops of their rumps. It is caused by organisms that are present in the soil everywhere. Every horse is exposed to them and horses with a compromised immune system and less than healthy skin are most likely to get it and get it worst. Horses with good levels of Vitamin A just won't get it.
If you have a fungus 'going through a barn', it is more than likely a pathogenic one that DOES need to be treated and equipment also does need to be sterilized. We have used a Captan solution that is much more mild on horses and hands than bleach. Captan is a garden anti-fungal.