Lots of snow there for sure....but are there any hills big enough to ski haha!!I am located just south of Buffalo NY in "Ski Country". We can see all 4 seasons in a single day here.
I too live in a lake effect snow belt, the snow loads and depths, not to mention the wicked west winds, are something to think seriously about as you build your chicken coop and run.
I'd extend your roof overhangs, even if you have to redo some stuff, to provide good ventilation protected from the winter weather, leave the eaves open but covered with 1/2" hardware cloth.
You say you plan on free ranging, but... not only might predators make that too risky at times, but they don't care for deep snow and may not go out in it. 4x8 for 8 birds is going to very tight during those days long storms we deal with. Chicken Cabin Fever is real, and it can be ugly. You're really going to want a large run that is protected from snow and wind. A strong solid roof and wind breaks installed for winter will make you and your birds much much happier.
Here's a couple good things to read as you plan further progress:
http://www.backyardchickens.com/t/1048597/ventilated-but-free-of-drafts
http://www.backyardchickens.com/a/how-much-room-do-chickens-need