Trains aren't hurricane proof either so we can take those right off the table. Of the rest, it takes very exceptional storms to blockade an airport for more than a few minutes. Delays that occur because of snow and fog are not because the commercial airliners can't fly in those conditions, but because the ground infrastructure can't clear the snow quickly enough, or because the reduction in visibility means increasing separation requirements on approach to landing and therefore reduces overall throughput. In places where it snows a lot there exists sufficient infrastructure to handle it (Chicago, Denver, Moscow). Even thunderstorms are not typically a big problem for commercial airliners and their airports; the controllers declare holds while the storm passes directly overhead and they're back in business in under an hour. And hubs that systematically are hammered by storms aren't hubs for much longer, a luxury that any railroad executive would kill for.

This is particularly impressive if you compare average airliner delays to average Amtrak delays.

Modern airliners are remarkably good at handling typical bad weather.

Even volcanic eruptions crop up with surprising frequency and result in vast disruptions to air traffic. Those disruptions can last for weeks and can shut down a single hub or potentially multiple hubs across a region depending on which way the ash cloud blows.

As an example, every few years the volcano on Bali comes to life and hundreds, if not thousands, of flights get delayed or canceled.