Hi,
There are many factors involved with running in cold weather that would impact your body in terms of asthma, muscle fatigue and blood sugar. I don't think a study has been done reguarding diabetics running in cold weather but I can say that the metabolism of lipids, carbs and proteins is altered by the temperature of the muscles.
Please find below a link to a study carried out by the U.S. Navy. It takes a lot of reading but explains the effects of cold on our ability to exercise in cold weather.
http://www.dtic.mil/dtic/tr/fulltext/u2/a240839.pdf
A decrease in the temperature of the air going into your lungs causes the capillaries which help the oxygen enter the blood stream to contract. This can make asthma flare and also causes a shortage of oxygen to muscles causing fatigue and altering the way your body gets energy increasing lactic acid and placing you in the same physical state as you would be at the end of a really bad asthma attack or during hyperventilstion. I personally cover my mouth and nose during cold weather which seems to help my asthma.
Could I suggest warming up in the house until you have a raised heart beat and your muscles are really warm. Not just stretches, I mean star jumps and running on the spot with arms pumping. Dress warmly with legs covered, gloves and a hat. Really hydrate before and after and see how you blood sugar does? Dont forget to eat salt if you perspire excessively.
If you can't get it stable swimming is an excellent alternative in cold weather which I would really recommend or a Pilates class to work on core muscles until the weather warms up again. If running is really the only excersise you would consider the local leisure centre or gym will have a treadmill.
I would be very interested to know your findings on this matter.