Besides the reasons already listed:
Keeping your gas tank full as much as possible means less air in the tank, means less water will form in the tank due to condensation.
Up here, driving with minimal gas in your tank is an invitation for increased water in the tank from condensation. In the winter, if water in your tank freezes and blocks your lines, your vehicle won't start.
In fact the gas up here contains gas line antifreeze (which you can also buy separately and put in your tank) in order to prevent this condition from occurring. But even this won't prevent the accumulation of water in the tank, if the gas level in the tank is always low.
Having a full tank means more operational time 'til empty - common sense, and important if you ever get caught in an emergency situation, a traffic jam, or otherwise stopped/stalled, especially in a snowstorm, or other winter condition - it means that you'll be able to keep your vehicle running that much longer, and it also means you'll have heat for that much longer.