A sloped roof, with all the snow in CNY, you want. You DO NOT want a flat roof. In fact, I suggest metal roofing, it is easy to put on and the snow and rain slide right off. But make it steep enough. I will send you a couple of picture of the housing we have built and you can see it doesn't take a lot, but you need to give it somewhere to go. Otherwise, you have to overbuild to compensate for the weight, and who wants to bother with that?
Next item, it is not the cold, but the moisture that will hurt your birds. I built one insulated coop, but it is actually my brooder house for chicks and needs to be insulated to raise chicks in the colder months. The adult birds are in UNinsulated housing. In fact, my big house will be open in the South ALL WINTER LONG. You can search on here for Woods Open Air Coops and find a thread about it. Chickens are hardy, for most breeds and you have good hardy breeds there, especially the Buckeye who was bred for your climate. If moisture builds up in the coop, then you start seeing frostbite, you start hearing wheezing and coughing and you invite illness. Keep it dry, keep it WELL VENTILATED and you shouldn't have any health issues.
People make the mistake of thinking that if they are cold, so are their birds. Chickens give off A LOT of body heat. If you don't believe me, pick one up and feel under the wings, even in winter it is hot. They have feathers that they fluff up to increase their "R-value" and it helps them keep that heat in. There is another thread on here that a BYCer in Alaska posted about keeping chickens in cold weather. They don't need additional heat if they are adult birds. Just a dry, safe place to go. You need to provide shelter, but don't get carried away with building something that makes YOU comfortable.
I live in SE Minnesota now, but grew up in WNY. Anyway, I booted my chickens outside every day but the 3 absolute coldest last winter. I fed them outside, and if they wanted to eat, they had to come out. They did great! What helps them even more is to throw a bale of straw for them nearby. They will have it pecked and scratched around in no time. It is good activity for them in the cold months when they don't have anywhere else to scratch and peck. It makes them happy and gives them some exercise. In the spring, I get a fork and put it in the compost