My experience, fox had come into barn and died, one dog rolled in spot before I could clean it up, both dogs got mange: dogs were treated with a dose of nexGuard (they had been on soresto collars per vet recommendation and purchased through vet - this was a few years ago now when soresto was new-ish and the vets seemed to like it as a flea/tick med at the time.) and a bath regimen with special shampoo/specific time to leave it on before rinsing instructions for about four weeks. Note that they were misdiagnosed first visits, so it got bad before figuring out it was mange. The cultures kept coming back negative, which I am now aware is common false negatives with mange testing.
Because dogs shared my sleeping spaces and couches etc, and it had been going on for a while by this time, as a precaution mostly, I was prescribed permethrin cream to apply topically, instructed to put on everywhere but the eyes.
I was told had the dogs been on nexGuard, they would not have contracted mange as it would have kept the mites in check. Soresto collars were tossed, and they were on nexGuard from then on.
The house had to be treated, similar to what they tell you to do for lice. They did not give me any instructions for the barn or horses though.