Might try a portable mister for the chickens and Dawg. We got an Orbit brand portable misting stand from Lowes. Ran a hose to it and placed it a spot shaded by some trees. Put the mister/hose connection over a storage box lid to catch any leaks. Our girls stand in the mist about all day long and wade in the water-filled lid.
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How well do those work when it‘s already danged humid out?