The biggest problem with Arizona is all the folks from the NE who moved here to get away from the NE, and now are trying to turn AZ into the NE. The second biggest problem with AZ is the folks from California...or maybe that is reversed.
"Cruel neglect" means to fail to provide an animal with necessary food, water or shelter." 13-2910 - Cruelty to animals; interference with working or service animal; classification; definitions
Note the word "necessary".
According to the OP:
contacted the Humane-Society. I have
contacted the state and they have informed me that "There is no law that requires these animals to have shade."
Are you kidding me???? Why not???"
Given the number of trail ride places that leave 20-40 horses tacked up with out any shade all summer long (which is disgusting, IMHO), I'd have to guess shade is not considered necessary.
I suspect the Humane Society knows the law.