Well...I was mostly talking about expanding the roof line if you were planning to leave it mostly wire. If you're going to box most of it in, then keeping the rain and snow off won't be an issue, so I'd leave the roof as is.
Can you get some better pictures of the structure? When I click on your pics, they stay small, so its hard to give advice.
But in general, if you get snow/winters, I'd add plywood to most of it, other than a small area at the roof peak to leave for ventilation. I'd have "window" openings on two sides (wired with hardware cloth, NOT chicken wire - chicken wire is great for containing chickens - but NOT great for keeping raccoons and other critters away from chickens). Fender washer and screws work well for securing hardware cloth. I'd screw plexiglass over the screened windows in winter time.
Will you be able to get that much roost space inside and still have space for them to flap up/down onto their roosts??? Ideally, for 12 birds, you really want a coop that's about 48 sq. ft. although folks in mild winter areas are often able to get by with smaller coops, allowing only 2 sq. feet per bird. So you might be able to swing a 24 sq. ft coop. If that coop doesn't offer enough space (not NOW - but when your birds are adults) - you might remodel to make the coop wider now - easier to make changes when the coop is at the rough stage as yours is now...