You wouldn't. You'd work to get ventilation and draft blocks in it.how do I insulate this (we’re in New England with cold winters)
You will need to put a pair of equally spaced studs in the back so you have something to install a piece of exterior grade siding on. I would frame out two more windows on that side too. Install the windows top hinged front and back so you can suspend them open during the heat of summer for breezes that will blow right through and across the chickens.
I like @rosemarythyme's suggestion to roof over the existing structure but I would use a tinted polycarbonate to keep the weight down, permit light to enter, have a slippery roof that is not easy for critters to climb on and would not be thermally conductive and condense water during winter that would not only drip back down on the bird but onto the wood to which it is attached which is likely just painted kiln dried.
Buy sheets that will extend about 3" past the roof slats for a bit more overhang. Unsupported polycarbonate won't hold weight so you don't want to go too far past the wood support.
Also as Rosemary suggested, the entire structure should get 2 coats of the best quality exterior grade house paint that you can afford to protect the wood. I would also get some of these
I would also build bump out nest boxes with a front panel drop access vs. one where you have to lift the lid. When you have to hinge the back of the lid (box roof) where it meets the siding, it always leaks where you attach the hinges because you cannot effective flash the siding/hinge joint.