Your coop is 4X8'. If one of the 4' end walls face south. You could remove the sheathing, and have a hardware cloth screen wall. That would vastly improve ventilation, and add some free light in there. Now, if the south facing wall is one of the 8 footers, you could open half of that and screen it, and end up with the same improved result.
I have found, if the coop is properly ventilated, after it rains, and some blows in, the coop will dry in a short time. (Unless you live in the pacific northwest, and it rains for weeks, then the coop will most likely, stay kinda wet). Also, the hardware cloth itself blocks a lot of the rain from blowing in. My coop is pretty much wide open. Open wire covered front wall (South facing), along with 3X3' side windows, that, when opened, are only covered with hardware cloth screen. The upper windows are hinged at the top and open out. So they keep most rainfall from coming in. When all the windows are opened for warm weather, I never run out and open and close them, according to what the weather may do, rain forecast or not. If it rains and some blows in, the coop always drys out.
Drafts can be a problem. But don't get too hung up on them and worry. They can have a little air movement in the winter. Especially in your mild winter climate. As long as they are not living in some kind of wind tunnel, with the air blowing their feathers up, there is nothing to worry about. They are like little furnaces, wrapped in down.