Yes dusty hay can cause cough. You can dab a little vicks at the nose to see if that helps. But if their barn is always dusty then you need figure out ventilation to help that.I have 2 Nigerian Dwarf does and a buck who have started an occasional cough. No other signs of illness and they are eating well. They are in the same barn as cows but have a separate area. The cow hay is somewhat dusty. Could this cause a cough?