Check the bottom seal
A cracked or flattened bottom seal lets in cold air, water and mice. If you can see daylight under a closed door, the seal needs replacing.
Lubricate moving parts
Use a garage door lubricant on hinges, rollers and springs. Avoid heavy grease, which thickens in the cold and attracts dirt.
Test the safety features
Place a piece of wood under the door and close it. The door should reverse on contact. Also wave something through the safety sensors while the door closes.
Book a tune-up
A yearly inspection catches worn springs and cables before they fail on the coldest morning of the year.