https://mashable.com/article/wind-turbines-texas> The reality about wind turbines, however, is they regularly operate in frigid conditions and can be weatherized to perform in wintry extremes. That's why they work in places like Sweden, Antarctica, and Iowa (over 40 percent of Iowa's electricity comes from wind). At times, some turbines (particularly those that aren't weatherized like many in Texas) are temporarily shut down during excessively icy conditions, wherein other energy sources, be it nuclear, solar, gas, or hydropower, are meant to pick up the slack.
This piece is slightly out of date now, 58% of Iowa’s power in 2021 came from wind per recent EIA data.
https://www.eia.gov/state/?sid=IA#
With regards to your fossil generator question, Texas experienced a loss of natural gas and nuclear generators during their 2021 February freeze due to a lack of winterization.
https://en.wikipedia.org/wiki/2021_Texas_power_crisis