Growing up in Michigan if I wanted to run year round I learned to adapt. When I worked in Antarctica and wanted to train for the marathon at McMurdo Station decently enough I learned you can run in just about any weather, but there are risks. Windstopper makes a world of difference. Always wear two pairs of underwear, or a pair of underoo and a pair of running shorts, and layer a pair of windproof running pants over those. Windproof gloves are key, as are Gore-Tex shoes and a fairly warm pair of socks. A face mask with a nose vent allows you to wear ski goggles, and a winter had with ear flaps makes a world of difference. For the upper body a compression top, and a cold weather running shirt with thumb loops in the sleeve and covered with a Wind Stopper jacket makes it complete. It's an expensive kit, but I've managed to run in -10 below with a fair wind chill comfortably. If you get ice on your mask scrape it off, and be smart enough to bring some hand warmers in your pockets in case your hands get too cold (nearly lost some fingers once when I forgot this step). If it's real cold or a long run being a second face mask for when the first freezes up, and possibly a second pair of gloves never hurts. Running in ski goggles is great if you have the right tint. People will think you're nuts driving by, but it's actually quite comfortable.
In short, there's no such thing as bad weather, just improper gear.