Certainly, if you have a cold or the flu, I would not recommend exercising. Patients ask all the time, “can I still exercise, even though I am sick?” Keep in mind, most infections are viral, and part of treating a viral infection includes rest. Even if you have a bacterial infection, it is best to rest, because no matter what is causing the infection, you are always dehydrated and exercise is going to make this worse which makes your recovery harder.
Asthma is caused by your body reacting to outside elements or allergens. Extreme weather is never good for exercising, but if you keep a few things in mind you may be able to exercise without causing an asthma flare.
In the winter the air is colder and drier typically. When you are breathing in this heavier air you may notice that your lungs burn. Normally there is a small layer of mucus in your lungs that keeps things in check, but if you are breathing in the cold dry air, that small layer of moisture evaporates and in turn you experience that burning feeling. Breathing in the cold dry air takes more of an effort for your body and it can trigger a histamine reaction, which is similar to what happens when your lungs are exposed to allergens. The histamine reaction will cause your body to produce more mucus which in turn makes your airways smaller and makes it harder to move air. Increased mucus can also make you to be more susceptible to getting infections.
Keeping all of this in mind, it is recommended that you try to breathe through your nose as much as possible and try to make the air that you are taking in more moist by either wearing a mask or breathing through a scarf. Breathing through your nose also helps your body combat infections, because you have little hairs in your nasal area that will kick out microbes to keep you healthy. Make sure you are well hydrated at all times which also helps to keeps the germs to a minimum. It is also helpful to use your rescue inhaler 15-30 minutes before you exercise.
Additional things to keep your asthma stable during the winter would include getting a flu shot, avoiding sick contacts if possible, washing your hands often, vacuuming/dusting frequently and washings sheets and blankets in hot water once a week. Asthmatics are more prone to asthma attacks when they get sick, so taking precautions to not get sick go a long way. I am also a big proponent of 500 mg of Vitamin C in the winter to help avoid getting sick. But remember, if you do get sick, give your body the rest it needs to recover quickly and avoid exercise.