Ventilation is a MUST. Even in the coldest of temps, you need ventilation in the coop, up high above roosts, so there's no drafts on the birds, but so ammonia and moisture. can be released. Most chickens do well, even in the coldest of temps, as long as wind isnt blowing their feathers when they roost (hence ventilation above roosts). You will be facing health issues, especially if you're going to keep 12 birds cooped up, if you don't add plenty of ventilation.
It's not that chickens "can't" go out in the snow, many just won't (mine won't- I have to shovel an area for them, if they're going to come outside of the run). The purpose of the run is to have something - a larger area - covered that they can go in that isn't the coop. Last winter, I didn't have a proper roof on my run so I covered it with huge tarps to block snow and wind, but left some ventilation in the run as well (again, above where the chickens would stand).
If you're able to post pics here, many people will be able to help give you ideas on how to improve the coop/ventilation/add a run.