Your garage door might stick because moisture along the bottom is freezing to the concrete below, freezing the door to the ground. You can prevent this problem by coating the bottom of the door with a water displacing spray. Before you coat the door, lift the door up so you can access the bottom ridge and wipe off any dirt, debris and moisture, and clean the concrete below. Pour some table salt over the area where the concrete meets the garage door. If you notice the door is starting to stick, reapply the spray and pour more salt immediately so it doesn't freeze completely.
Ice can form on the rubber or weather stripping on your garage door or its track. The ice freezes the door and prevents smooth opening and closing. If you coat the rubber with floor wax or water-displacing spray, the coating prevents the ice from sticking to the rubber and lets the door slide more easily. Don't use products containing petroleum because the petroleum can damage the rubber.
If your garage door or frame is painted with latex-based paint, the door might stick because both the chemicals in the latex paint and on your door allow for flexibility and may stick to each other as a result; this is referred to as "blocking." The problem is usually worse after a recent coat of paint, and some latex-based paints don't set properly in cold temperatures. The sticking should resolve itself over time, but if you have a repeated or prolonged problem, you might have to remove the latex paint and repaint. Use an alkyd paint or an acrylic paint designed to stop this type of blocking.
If you have an automatic garage door opener, the door might seem like it's sticking in cold weather, but the mechanism might just be struggling because changes in pressure affect its power. Most mechanisms made over the last decade have adjustment settings found on the back of the mechanism or underneath the lens of a light. Check the manual that came with your garage door opener for instructions on adjusting the pressure. No matter what the adjustment method is, make sure you raise pressure in the smallest increments possible and test the door after each adjustment. Unnecessary pressure can damage the door.