Chickens and horses do fine togehter. The chickens will clean up after the horses grain eating, and behind them as well, and the fact that they spread manure is good for the horses, it reduces the worm cycle considerably and lowers the fly population as well. If the horse manure is piled anywhere they will scatch therough that as it composts recucing the fly population even more, although Muscovie ducks are even better for that purpose.
Having chickens around horses makes them calmer and better mounts. While they may be spooky to the noisy flapping that goes on at first as they get used to it they become a safer horse to ride especially out on trail as a grouse or other wild bird flying up will not spook them. The horse may act irrate towards them at first but I have never had one not just settle down and accept my chickens in a week or so.
The concern over the dust is valid only if the chickens and horses will be confined in the same airspace, such as being locked in the barn at night. Have your own night shelter for your chickens seperate from the horses and your good.