...As long as rails and bed are there, a train will make it thru. In contrast, planes often don't fly even though their runways may still be physically intact.
Rail travel is dependent on lots of things other than the physical condition of the track. Notably, getting utility power for signals and grade crossing protection, maintaining communications to dispatching centers, and even getting crews to the trains. If anyone of those things is disrupted, trains stop.
Every mode has its plusses and minuses for foul weather operation. Air travel can be severely affected by even moderately bad weather at end points, but is unaffected by bad weather in between. Rail can get through some pretty nasty weather, but a severe storm anywhere along the route can disrupt the entire route. A storm in Chicago can disrupt United Airlines for a day, but not bother Amtrak. But a blizzard in the Rockies can cancel the Zephyr for several days, and not impact flights from Chicago to San Francisco. It's all the nature of the travel beast.