I can't speak for the smaller airlines but wrt to my airline when there is a large wx event (hurricane/snow storm) bearing down on a hub they will run ops up to a certain point then get everyone (airplane wise) out of town.

For example: bizzard headed for NYC, wx people say the crap will hit the fan at 8 pm Friday and will snow for 30 hours. The last flights in/ out will be about 5-7 pm Friday. At that time at an airport like lagarbage there may be 1 or 2 planes per airline left on the ground so snow can be easily removed. Basically get everyone away from the wx event then when it's gone send them back in. In the case above by Sunday morning the first flights will start arriving and by the end of the day Sunday or early Monday a regular sked will be restored.

The only down side is that there are many CXd flights so all flights for a few days after will be fuller than full as they clear the backlog of stuck pax.

IMO this method is the lesser of the evils. Many years ago we'd try to run as much as possible thru a wx event. You wind up with airplanes and crew stuck everywhere. Crews with planes but times out. Crews that can work but their plane diverted inbound so no jet available. Crews stuck in whatever hotel. It would take days just to put the sked back together.