we have ours wired - too many dogs, cats, foxes, mischief makers!
after the wet summer & winter, it became a mud bath very quickly.
So I'd recommend a roof, if you're thinking wood maybe just do the bit near the coop to stop it being too dark.
(No coppers about?? the roads around us were tar-sprayed a few weeks back, the council didn't take down the corrugated plastic signs everywhere for AGES, so when the clips were getting abit tatty.... I liberated a few! they make brilliant rooves on the chook run. typical blooming council, the day after they sent round the roadsweeper and a bloke to collect up all the signs!!)