I would definitely do both sides. Ventilation works better if on opposite ends. As far as high winds and drafts, a cheap and effective method is to tack up furnace filters over the ventilation. I've never had to with my setup. If we had high winds and bitter cold, I just reduced the opening on...
Like I did with my coop. I cut the siding to make the opening, but used that piece as a windbreaker and to stop driving rain. First pic is during the construction phase before HC was added. In the second pic you can see the seam just about the window.
I second opening up the areas below the roof in the second picture. When you remove that siding piece, I'd hinge it from the top to act as a rain deflector.