[carpdad]

Steel doors have a flange that channels the water from top and sides. You need something like it also. Steel doors also have some kind of rod that keeps the door from closing, which is another kind of safty. Hinges on your doors could get damaged if allowed to open past the allowed open position. When open, does the door sort of rest on the frame and hang over?
PT lumber need to dry or paint may peel quickly, if paint was planned. Usual recommended dry time is 6 months. Was the wood choice because you like the look or budget? Even if you like it, wood isn't a long term choice as such. Area under the battens will rot out faster, even if PT, because it will trap water.