Greetings from Michigan! We get snow too.
You have already received such great advice that I don't have much left to offer. I do take to the treadmill in smaller breaks (less than 10 miles) when I have to. Like the good advice from others, I invest in a great quality cold (sub zero cold) running gear, tons of smart wool socks to keep my feet warm and dry (which I wear year round by the way--hello, sweaty feet?). I also use "hot hands" for my feet and hands when I need to. They can be a life saver in the gloves or socks. I do wear gortex shoes (Brooks Ghost in gortex) in the snow, rain or sleet. I put tracks on for ice.
I also take advantage of indoor tracks when I can. But mostly, unless it's very icy out and I am concerned about a tumble, I try to take it outside as much as I can. Best wishes in your training!!!