Apparently natural gas isn't easy to store, so basically there's not a lot of buffer, and everything needs to stay online or there won't be any natural gas to burn at power plants even if they were winterized, which some of them were.
I think some power plants may have even just shut down because natural gas was available but too expensive, and they weren't under a legal obligation to keep producing electricity.
Point being, to solve the problem, winterization of plants is just part of the problem.