Interesting that everybody looks to the Airlines when there's a problem such as this.
Jet Blue is a "Low Cost Carrier!" They keep their costs low by paying their agents $10 an hour and then understaffing the $10 per hour people. These untrained "crew" members are supposed keep everything moving and keep everyone happy but when weather moves in they are simply overwhelmed.
To keep costs low NO JetBlue aircraft have their own airstairs. This prevents them handling flights anywhere but at a gate. Gates cost money, and in bad weather are all occupied. They can't move off the gate, to be deiced and on their way because the FAA can't handle the volumes and glycol only has an average :15 holdover time between the time it's applied and the time the plane should be moving down the runway on its takeoff roll. The only way they could work at a remote parking location is by supplying stairs to the plane-another high cost item, so that's when gridlock sets in and people get trapped on planes for hours.
Since everyone bitched so much about "airplane food" all the catering trucks that were capable of resupplying aircraft, even off the gates, are gone. Even if they were still around, this is another cost item. JetBlue is not catered by trucks so when they get stuck, and there are no stairs, there's no way to resupply. It's also an FAA rule that they can't refuel, without stairs or a jetway so as to provide a fire exit. This prevents them from getting some fuel so that they could move to another airport for more complete service. Lavatory service is one area where technology is unchanged. As long as they can find someone to drive the Lav Truck to the plane, they can be dumped and refilled with fresh flush water, assuming someone plugged in the tank heater to keep it from freezing, but JetBlue relies on their "business partners" to do that so the short-staffed, inexperienced "crew" members may not have been aware that remote Lav Service was even a possibility.
When the weather's good, no Air Traffic delays, no mechanical problems etc. the airlines can operate but short of that you play your cards, take your chances, and maybe get your mug on the news to tell all the other frequent flyers what a "terrible" experience you just had. But you also "saved a bundle" on your ticket!