https://www.wthr.com/article/news/local/dangerous-heat-causi...
https://www.wdrb.com/news/a-southern-indiana-utility-warns-r...
I'm from EU, a relatively "cold" (French Alps at 1030m) place but definitively not that cold (peak cold -25℃/-13℉ in early morning, -8/10℃ (14/18℉) during the day between January and February), with a new home witch means well insulated, with a proper VMC, water-water heat-pump etc, and well... The MINIMUM load during night and early morning is around 1kW. IF Sun shine during the day, well, the load is not much an issue from 9h30 AM to 3 PM, but for the rest is on grid.
Of course old homes heat with gas/oil/wood/* so need far less electricity (still IME a bit more than 2-300W base load though) BUT apart of wood coupled with large hot water storage (to been able to sleep instead of charging wood every hour) if you are not living in a relatively cold place I doubt you have a 6-12 month gas/oil/wood reserve at home and during such "cold episode", being very rare so far, getting new "fuel" would probably be not that easier...
I've made a small p.v. with lithium storage as a very expensive UPS for the house, being relatively autonomous in summer I hardly can be autonomous in winter: in some RARE winters like the last one where Sun shine almost all day I can survive a day to the next cutting the heating depending on battery SOC, but in case of a day without enough Sun light I'm still on grid or on emergency generator backup... Having a real autonomy IME is more a dream than something feasible, at least something feasible at human prices because spending the price of a house just in batteries who might last at maximum 10 years for some rare episode is not really a sustainable price...
About natural gas: if the outage is widespread I doubt you can get it: who pump it in the pipeline without energy?
Natural gas has not gone out here for a while and is a much larger issue if it did. Gas company would have to come out and lit all the gas appliances. I assume they spend a lot to prevent that cost and can use themselves to power their infrastructure.
Sure, but they were (and still are?) like so because normal climate conditions do not demand that. Being able to sustain "any climate" is damn expensive, giving a certain margin while designing a home is natural, the home itself have a value, but going much further it's simply too costly at best. Now, insulation is good BOTH for hot and cold, but for instance if with mild insulation and p.v. you can live well because it's hot only during the sunny day you hardly invest in real insulation.
Beside that during a snowstorm a p.v. does not produce so if you have a battery you can recharge it on a generator, but no more than that. It's far cheaper to run than a 24/7 generator online, but it's still roughly expensive and demand a significant quantity of fuel you normally do not have at home.
About natural gas, well, I suppose their infra are designed to be "a bit" disaster proof, but how much and how in realty it's hard to tell up front. I remember for instance that a day in my original town a flood happen and for some reasons water penetrated the piping infra. Gas completely stops for two days. They have had some water pumping systems for condensation and other phenomenon but it wasn't ever used and even those who have designed it have designed for clear water without mood and sand. Apparently an event that break a pipe and push water in the net was not much assessed. Most physical infra, even critical ones, never have nor can afford doing Chaos Monkey things on their systems...
Been though those, I don't really think "storm knocks out power lines" is the kind of problem people are talking about when it comes to grid reliability though. No amount of coal is going to keep the line from getting cut.
Once we have a bunch of storage, and are used to doing grid ops on lots of intermittent generation sources, grid reliability will go up because a power line going down will have lots of potential mitigations that are not possible today.