How should people with asthma take care of their health and prevent attacks during cold winters/cold winds?

Cover nose/mouth. Cold air is a know trigger for asthma symptoms. The nose is great at humidifying and warming cold air, so you should always try to breath in through the nose and not the mouth. Covering your nose and mouth with a scarf or mask is one way in which you can go outside in the cold and prevent the airways from being triggered to react.
Don't forget... ...The decreased ventilation of the indoor air during the winter. More dust collects, more smoke stays inside. Now would be a good time to quit smoking!