In the winter, your car's fuel line can freeze up very easily. This usually happens when the gas level is below half a tank. When your gas tank fills with air, the moisture in that air can freeze into ice which clogs the line. This usually happens when the car is sitting for a few hours in the cold, but the fuel line can freeze while you are driving if the conditions are cold enough.
If your car will not start on a cold morning, a frozen gas line is one of the most common causes. Once the temperature is warm enough, the line should unfreeze and your car will start normally. Push or tow the car into a garage to help it unfreeze faster.
Not Turning Over
If the line is not completely frozen, your car's engine may turn over but not start. The car is not getting enough fuel to start, or a little fuel was still left in the line before the tank froze. Again, get your car somewhere warm enough for it to defrost, or simply wait for it to warm up.
Sputtering or Stopping While Running
If you are driving in extremely cold temperatures, the gas tank can freeze while you are driving in spite of the heat the car is generating. This causes the car to sputter or stall while you are driving. This can also happen if ice crystals started to form in the gas line without blocking the whole tank.