When the flight cancels you can take the replacement flights offered by the airline or you can get a full refund. You can choose to have the refund in cash (well, returned back to the original credit card) and you do NOT have to accept the refund in airline credit vouchers, though that's what they'll probably offer at first.
If you want to be rerouted, do your own research and decide on what flights you want to be on. Know what options are available when you talk to the airline. You can also standby for earlier flights which are showing as full. It isn't unusual for seats to open up on those flight by departure time.
If the airline can't provide acceptable options, you have the right to a full refund and make sure it goes back to the original form of payment.
When weather impact an operation, overall system capacity is reduced. Flights must be delayed and cancelled because the system is no longer capable of handling the volume. These are still weather (uncontrollable) cancellations under DoT rules.
If it is an airline's hub airport that is impacted, switching to another airline, with a different hub, can often work. The non-hub airline had relatively few flights at the impacted airline so that airline is not as significantly impacted by the weather.