Yes, chicken, or any fowl's droppings can make your horses sick. Several viruses and bacterial infections such as salmonella poisoning can be transmitted to your horses if they ingest it bird droppings.
I would insist that my neighbors confine their chickens. Meanwhile be sure not to use the soiled hay. One solution is to cover the hay so the chickens cannot get to it until the problem of keeping them home is solved.
I hope this has answered your question. Let me know if I can be of further assistance.
Donna C. Smith