The job of managers is to create a robust system that delivers value to customers. A system that fails constantly (fails during the continual variation the system faces) is a failed system. Bad weather is part of the variation airlines face. Any management system has to cope with the variation that it faces. The management system must be designed and managed so that the organization successfully delivers value to customers under the conditions the organization will face.
The air travel system in the USA is a disgrace for so many reasons it is hard to catalogue them all. One, of many, is how fragile the system is; causing massive (nation-wide) customer harm multiple times a year due to weather. Weather is sometimes bad. If your organization fails when there is bad weather, fix that problem (make your system robust in the face of bad weather), because you are not going to be able to fix the weather to let your un-robust system be effective as it is.
Instead airlines only response seems to be to get their friends in government to approve anti-competitive mergers to eliminate competition and allow failed organizations to become even larger and harm even more people. Airlines should design robust systems that work in the environment they will face (which they don’t do now).
Their planes don’t fall out the sky when they face bad weather. The engineers behind designing planes have made them very robust. Pilots have been trained to handle variation they will face. And yes, the system has been designed with adjustments to avoid flying into conditions that are risky.
The safety of the air transportation system is very good. The management of airlines in most every other aspect is pitiful, and has been for decades.
The managers running the airlines have done amazingly bad job of creating robust organizations capable of delivering given the variation they know they will face (weather, mechanical problems, IT problems, etc.) for decades. Poor management is the cause of these failures that result in harm to customers. Weather is not the cause. Poor management, over decades, resulting in incredible fragile systems that constantly punish customers is the responsibility of the airlines. And they have done an incredibly bad job at creating a robust system to deliver value to customers.