Extreme winter storms have increasingly disrupted power grids, leading to widespread outages and severe economic losses. Gas-fired power plants are particularly susceptible to these extreme cold events. This study investigates the impact of extreme cold weather on gas-fired generator output and proposes a Bayesian probabilistic model to predict generator net available capacity under severe winter conditions. The model incorporates key exogenous variables, including temperature and electricity demand, to capture the relationship between cold weather and generator output. Our findings provide valuable insights into the resilience challenges faced by gas generators under frigid temperature, emphasizing the need for data-driven approaches to support proactive planning and mitigation strategies for future winter storms.