Make sure that the wood that is in contact with the ground is rated to be in contact with the ground. Not all treated lumber is created equally. Treated deck material, if in contact with the ground will rot in less than a year. Take a look here:
http://spartanburgforestproducts.com/our-products/treated-wood/levels-of-treatment
OSB absorbs moisture like a sponge, if you are going to use it for an exterior application take care that it does not get wet. Even if you paint it, water will seep into the joints and cause them to swell and weaken over time. OSB is wrapped in tyvek or vapor barrier before siding is applied when building a home. From wikipidea: "OSB panels have no internal gaps or voids, and are water-resistant, although they do require additional membranes to achieve impermeability to water and are not recommended for exterior use." Although there are different kinds of OSB, one of which is coated one one side, the joints and any cut edges are still susceptible to moisture penatration.
Painted T1-11 is your safest bet to use on the sides of a coop and is manufactured to be used in exterior application (no additional siding would be needed). This stuff is thick and sturdy and is in the median price range.
http://www.t111siding.net/
You could also use corrugated metal roofing as siding material, secured properly, this will stand up to any weather. However, metal material is a pita to work with sometimes, so make sure you've got the right tools and you wear gloves.
Plain kiln dried 2x4's for wall and roof framing. OBS plywood on the roof covered with paper and shingles. Or, skip the OSB and use furring strips on the rafters and metal roofing. Both are good for hard weather.