Only immature mice can get through 1/2" hardware cloth. As they mature, they won't fit any more. And I can't imagine a snake small enough to get through 1/2" being much of a danger, at least not in the USA.
Mary
We also use saplings or tree limbs, bark on, not dimensional lumber. Chickens were designed to roost in trees, after all.
Some of our birds roos eight feet up on the rafters, which are 4" fence posts in the original structure.
I think location matters most, because of social order issues...
Window screens won't keep any predators out! You will need hardware cloth, at least.
Young mice can get through 1/2" hardware cloth, but only when very young. As near adults, they can't. Rats and weasels are a much bigger issue, and 1/2" will keep them out.
Here we added 2"x 4" woven wire...
Your metal shed is a great start, love it! Lots of ventilation, as mentioned, a dirt floor will be fine too. Predator protection! Make sure nobody can dig into it anywhere, and hardware cloth over every opening is essential.
With good ventilation, maybe the roof won't trap moisture, but...