A cold sore is the result of an infection by the Herpes Simplex virus. Once you are infected, it never leaves your body. For many people it just goes permanently dormant. But for some people it will 'wake up' periodically.
When it does, it will travel across your skin and attempt to reach your lips. if your lips are cracked or something, they will have a path inside and cause the symptoms you present.
This happens in winter because its much more likely for lips to get chapped and such in cold weather.
Though you can't cure Herpes Simplex, there are treatments to make the cold sores much less miserable when they show up. A doctor can help you with this. Usually involves topical anti-viral medicine, which speeds healing up.