I keep my coop kinda open in the winter. We live near Dallas Texas. I have it vented I guess you would say across the top of the walls near the roof.
If you are gonna get a huge draft in through those openings I would try to find a temporary way to cover them. I hang a heat lamp (the one I used for the brooder) in the middle of the coop. Then we have a small space heater in the corner by the roosting poles. I don't use either of them unless it's really cold.
You may want to clean out your shavings and give them fresh stuff to start out the winter. They will dust bathe more in the coop than outside once it starts getting cooler.
It got down to single digits here last winter, and I have a window in my coop that only got a garbage bag stretched across it--I was constantly having to fix it. If you are in an area where you won't get much below freezing, I don't think you need to worry about doing more than cutting the drafts on cold nights. I imagine plastic over the opening would be fine, but make it something you can put up and down, because you don't want to cut off all of the ventilation or you'll get sick chickens.