Nuclear plants may or may not be reliable, but outages at multiple nuclear plants are usually not corellated.
Solar is corellated around time of day on a large scale and cloud cover on a more localized scale. Lack of wind sometimes happens to fairly large regions; interconnections to farther away wind farms helps though.
Weather extremes outside the design can result in outages for all kinds of plants though, so a relatively geographically small and isolated grid like Texas, that has many plants unprepared for cold will likely have outages at plants of all types during a bad cold snap; a particularly bad heat wave might cause issues as well.
Solar is corellated around time of day on a large scale and cloud cover on a more localized scale. Lack of wind sometimes happens to fairly large regions; interconnections to farther away wind farms helps though.
Weather extremes outside the design can result in outages for all kinds of plants though, so a relatively geographically small and isolated grid like Texas, that has many plants unprepared for cold will likely have outages at plants of all types during a bad cold snap; a particularly bad heat wave might cause issues as well.