Hi, I saw your cross posting on the other thread (random pictures). I'm currently dealing with red mites for the first time, and so have recently been doing a lot of research. Luckily, we caught the infestation early, so it hasn't been too hard to deal with.
From what I've read, I don't think red mites can live on horses as many parasites are species specific. Wikipedia says that red mites in chickens are
Dermanyssus gallinae and will also prey on other bird species. They
are capable of biting other animals, such as mammals, and have been known to cause allergic reactions, but cannot live and survive on non-bird species. I suppose it is possible that red mites may have bitten a horse and caused an allergic reaction, but they will not be living on the horse.
If this horsey person has red mites making themselves at home on her horse, then it is an entirely different species and not associated with your chickens at all. They will be a type of mite or louse specific to horses. "There are two type of mites in horses,
Haematopinus asini, bloodsucking and the
Bovicola equi, the biting louse." This is from
http://www.horsecaring5.com/mites.html. She needs to find out how to treat these
horse parasites to solve
her problem. When I was young, we raised Thoroughbreds and had farm chickens roaming in and out of the pastures and stalls constantly. There was never an incidence or worry about cross species transfer of parasites. In fact, most people we knew with horses also had chickens. I think we would have heard something if anyone had had problems.
Red mites don't live on the chickens. They live in cracks and crevices in the coop and crawl out at night to feed on the roosting chickens and lay eggs. If they are in your coop, they will not be on your chickens in any great numbers when the chickens are out during the day. Check the roosts and walls of the coop at night with a flashlight to see if you have the rotten creepy-crawlies. If you do, you need to treat the coop. Washing the chickens will make them clean and smelling lovely, but won't help much with red mites. A heavy red mite infestation can weaken and even kill chickens, but you will not find them on the birds except at night.
Hope this helps!