Nothing wrong with using treated lumber for rafters, just not necessary. Using it on the sidewalls under hardware cloth is a good idea. Treated lumber is usually sold wet (and heavy) but will be about the same weight as regular construction lumber after it dries. Slabcrappy is right...you should use screws or nails that are specifically made for treated lumber. Either galvanized nails or "deck" screws. I like screws because it makes it easier when I change my mind. If using screws, drill a clearance hole, the same diameter as the screw, in the top board. Normally a pilot hole isn't needed in the bottom board unless you are screwing close to the end where splitting might occure.
Paul
Paul