What are the actual dimensions of the coop -- length, width, and height -- not including the nests?
Here is some general information for you:
The Usual Guidelines
For each adult, standard-sized hen you need:
- 4 square feet in the coop (.37 square meters)
- 10 square feet in the run (.93 square meters),
- 1 linear foot of roost (.3 meters),
- 1/4 of a nest box,
- And 1 square foot (.09 square meters) of permanent, 24/7/365 ventilation, preferably located over the birds' heads when they're sitting on the roost.
15 hens
- 60 square feet in the coop. 8'x8' is easier to build than 6'x10'
- 15 feet of roost
- 150 square feet in the run. 10'x15', 12'x12' or 8'x20'
- 15 square feet of ventilation.
- 4 nest boxes.
Since you live in an area subject to severe winters with significant snowfall you should probably plan on either having a large covered run or a significantly-oversized coop.
Here's a useful article on cold-climate chicken-keeping:
https://www.backyardchickens.com/articles/cold-weather-poultry-housing-and-care.72010/
The fastest, easiest solution would probably either be a hoop coop/run or a dog kennel conversion. Chainlink dog kennel panel are often available on Craigslist at reasonable prices.