Keep in mind that, unlike humans, dogs do not use evaporative cooling (we sweat) to keep cool. They pant through their tongue or find a cool spot to lay on. SO, humid air does not matter, just the temp of the air. You CAN use evaporative cooling like those that blow air out of an ice-filled cooler and the dogs will be happy.
You are talking major battery usage to run any AC (powered by A/C or DC doesnt matter), so it will be cheaper to run a generator than to do such damage to batteries. Anytime you deplete or use a battery it is damage. There are only so many "cycles" any battery can do and running an A/C unit will surly induce a deep discharge. Solar is of not much use unless you have a big roof covered completely with panels.
You will spend more on batteries due to short life than you will on gasoline.
I would look more into the personal cooling contraptions. The room does not need to be cooled, only the air blowing on the dogs. They will be happy sitting in that one cool spot all day long.
