We used spray foam insulation in all cracks, everywhere that two pieces of wood came together. And we used roll plastic, before we put up the studs around the entire coop. Then plywood inner walls. We put hay down into the walls, as we were putting up the plywood. I don't know if that's a good idea or not. We just did it, without researching so hopefully people here can tell you any reasons not to.
Our vents are between the rafters, with the eaves exposed, and we put little doors on each one with a hook and eye to close on extremely cold nights. The vent doors have plastic built in that closes with the door and seals it. We haven't had any problems at all down to minus temps, maybe -15. Oh, and we do put on a heat lamp when it gets down to about 10, but I've heard that other people don't and theirs do fine.
Our vents are between the rafters, with the eaves exposed, and we put little doors on each one with a hook and eye to close on extremely cold nights. The vent doors have plastic built in that closes with the door and seals it. We haven't had any problems at all down to minus temps, maybe -15. Oh, and we do put on a heat lamp when it gets down to about 10, but I've heard that other people don't and theirs do fine.