Nicky has had rain-rot twice now (last 2 years). Luckily just in small spots--inch or so diameter--I used a "pink" anti-fungal spray product from our local co-op. Active ingredient: benzalkonium chloride 0.15%. I only had to use it once or twice to get rid of the rain-rot.
We don't shave, and we don't blanket. Plus, Nicky likes to roll and get dirty.
I don't know about Listerine. Guess I'm a wuss, but that stuff stings my mouth when I use it. I can't see using it on a horse. (hmmm, I wonder if it would stain Nicky's white hairs to blue-ish?)