In the 2011 cold snap, the problem was all about frozen lines like the pressure sensing line that caused a problem yesterday for the nuclear reactor. Likely similar things are causing problems for natural gas.
The answer is weatherization of all these sources. Wind turbines work great in other settings with icing wind, you just have to have the hardware for it. Just like you have to have the hardware to keep your pressure sensing lines from freezing.
We are likely to experince more events like this before a single nuclear plant could be built. And the idea of building 30GW of new nuclear, the amount of gas/coal/nuclear that was lost, is so daunting that not even China is trying to build that much nuclear, and they're pretty much the best at doing it of anyone out there.
Honestly, building 60GW more of wind and solar, and 10GW/40GWh of storage would be a lot easier and cheaper than building 30GW of nuclear. Solar delivered an extra GW when it wasn't expected, wind dropped 4GW from what was expected, and gas/coal/nuclear dropped 27GW.