If you're subsceptible to asthma, cold air can trigger an attack - while the link between changing weather and asthma hasn't yet been fully explored, a rise in emergency room admissions and testimonials suggests a strong causal link.
Prevention is always better than using your puffer (though it's important to make sure you have it on hand, as simply knowing it's there can reduce panic, and decrease the severity of your symptoms). Here's some very simple tips.
First: stay warm when you sleep. Keep blankets on, use hot water bottles, put your nose and mouth under the blankets or ensure your room is well heated. This will reduce the likelihood of you waking up wheezy, or waking up in the night unable to breathe.
Take a scarf with you when you go outdoors. Breathing through a scarf can help keep your lungs protected from chilly air. Keep your torso well wrapped as well.
Drink hot coffee. Caffeine can dilate your blood vessels, is closely related to theophylline (a bronchodilator drug) and significantly improve asthma symptoms before you get to the stage where you need your inhaler.
If you're finding that you need your inhaler all the time even though you're making an effort to stay warm, it's worth seeing a health professional to rule out any other issues.