Your lungs will get used to the cold after a few runs outside in it. I started up again at the beginning of Jan. and it took me maybe 3-4 times out to get so that I could run and breathe normally. Stick with it -- it will get better if you keep at it! As others have said, layers, hydrate, and some sort of traction (I use Stabilicers instead of Yaktrax) are great helps.
Also, if you have access to places that rent equipment and there's consistently enough snow, I've heard great things about snowshoeing and CC skiing to stay active outdoors during the winter -- work with winter, not against it! I haven't actually tried them yet, but I'm hoping to go CC skiing soon, maybe this weekend. I live in St. Paul, MN, and you wouldn't believe how active people are here, no matter the weather!