What you have pictured will work fine if you cover it with wire, or hardware cloth. As you said, you have predators, so the chickens have to be secure. Nesting boxes can be as simple as a couple of milk crates with hay in them, or a couple of the small plastic totes with an opening cut into the side with hay in them. It won't hurt them if they get misted on during a rainstorm, except in the winter. During the winter, you can staple some heavy plastic around the sides, leaving a bit of the top portion open, so moisture doesn't build up inside, which helps against frostbite. I live in the central part of Florida, where heat is a major factor, and our winters are fairly mild too, so enclosing a coop is not a viable option unless you add fans, and/or misters to the coop, which is very expensive for those of us that are not in it on a large scale.