The short answer is this: batteries.
The longer answer is this: distributed systems.
The benefits offered by large-scale distributed systems is why states other than Texas have integrated themselves into power grids. High demand occurs at different times in different places, and a widely dispersed distributed system with multiple sources of energy production (oil,gas,coal,nuclear,hydro,wind,solar) helps to insulate the customer base from wild fluctuations due to vagaries in demand, weather, and resource availability. That means more stability in both the service and the price.
Power grids aren't perfect - people on the grids still get blackouts and brownouts. The Eastern and Western power grids are not 100% reliable or resilient to all forms of natural disasters. However, those grids are multi-national (Canada and US), and a good percentage of the power generation equipment is located in areas that get severe winter weather. The regulators and operators of that equipment wouldn't consider the four days of winter weather just seen in Texas as particularly challenging. Many of them look forward to that kind of weather and go out hunting and ice fishing and skiing and snowmobiling.
When I lived in Massachusetts, some streets in our town would lose power once or twice every winter. But it was always due to downed power lines caused by ice-laden tree branches. It was something the power companies planned for, and something people in our area knew could happen. We would just fire up the wood stove, put the tea kettle on it, and get out the cribbage board. I would venture to guess that people in Michigan have a similar outlook and have had similar experiences (although I'm not sure about whether cribbage is played very much in Michigan).
One more thing - getting power from wind is not something new. It's a technology that's been around for hundreds of years, and it will be around long after civilization transitions away from fossil fuels. And that will happen - there are countries today that get more than 10% of their energy from renewable sources, and the number of countries for which that is true, and the percentages themselves, are only going to go up.