Marine ply works best but it's become really expensive. I looked at marine ply, can't remember the exact grade but its full boats, when I was still thinking about building a coop rather than buying one for the field chickens.
I used some ordinary grade ply on a couple of the coops in Catalonia and the edges were peeling after a single winter. They were painted as well!
The bullet proof option I found was half inch marine ply covered with EDPM sheet over the roof and the EDPM sheet edges tucked under the roof and held in place with wooden battens srewd into the ply. Obviously screw length becomes critical here. I know.