Unfortunately, running in the cold is just one of those things. I've got very mild asthma but the cold always makes it act up. You should probably get checked for it just by your symptoms because they sound suspicious, or at least explain the symptoms to your doc. He could give you an inhaler to puff before you go run in the cold and that helps a lot.
Other than that, walk briskly first for about 15-20 mins to warm your body up and let it adjust to the cold air, PRACTICE BREATHING IN THROUGH YOUR NOSE ONLY -- this requires learning how to time your breathing while running instead of panting. You can breathe out of your mouth, but eventually get to where you don't need to. You'll notice you run better once you get it down.
That's all I can offer up, but you can take comfort in the fact that you do tend to run a lot faster when it's cold. LoL. You would die seeing army P.T. tests in winter. People strip down to just that little t-shirt and shorts in 20-something degree weather to do the run. I was hesitant but when I finally gave it a shot, I finished my 2-mile in just under 13:30.