That's generally true. Shut them down when the load is normally low. Then, there is the frozen pipes thingy.However......typically, generators do maintenance during off-peak periods. Some of the immediate generation shortage is due to a lack of available units due to the number of units on maintenance (many of these units cannot be immediately returned to service because they are basically apart).
ERCOT handles 85% of Texas grid. My son works for ERCOT and helped develop the computer model in use now. He tells people that my house will be the first on the list of rolling blackouts because he doesn't want to be accused of favoritism. He says that there have been rolling blackouts in Texas twice since the late 1980s.