A snowstorm is considered an "act of God" by the airlines, and a cancellation is therefore usually refundable, regardless of what kind of ticket you have. Although each airline carrier contract is different, a snowstorm is beyond the control of the carrier, and the airline is legally bound by the contract of carriage. A review of the airline's specific contract spells out the refund procedure.
If you choose to continue your trip despite a snowstorm cancellation, the airline is not obligated to give you any compensation. Speaking respectfully and politely to a ticket and gate agent, however, may land you with meal and hotel vouchers, phone cards or seats on another airline. Travelers with special circumstances and frequent-flier club members are often awarded extra perks, so it never hurts to make a request.
When the person working at the ticket counter informs you there are no flights available, make your own suggestions. Passengers willing to fly out of, or land in, alternate airports may discover seat openings available much sooner than the current delay. Investigate the possibility of renting a car to drive to another airport or having a friend pick you up.
Call the airline early and frequently to find out if your flight will be delayed or cancelled, and save yourself hours of waiting around at the airport. Find out about cancellations early to give you time to arrange for a different flight before the airline sends out the official cancellation email to the other passengers.
When at the airport during a snowstorm, large crowds of stressed-out people are certain to form. Avoid the crowds and contact the airline via the Internet or your cell phone for information. You will probably receive your answer quicker, while keeping a semblance of calm in the midst of chaos.