In my coop, the half round windows have hardware cloth and window screen over them. No glass. The HC is to keep out critters, the window screen is for bugs. The side windows are just for more light.
Chickens wear down coats. They can handle the cold very well. Oklahoma weather should be no problem. They may have more trouble with the heat in summer.
The pictures below show the roof overhangs that shelter the openings from the rain. It takes some really horizontal rain to blow in. That said, I did take advice from
@aart and cover the bottom half of both of the half rounds with furnace filter material. Air still goes through, but it'll stop rain/snow from blowing in.
I bought two of the cheapest furnace filters I could find. I took off the cardboard frame, cut them in half, and stapled them over the bottom of the windows. I don't have pictures of that.