Extreme winter weather has repeatedly disrupted gas-fired power generation in the United States, yet the plant-level data needed to systematically quantify outage risk remain proprietary. Using publicly available weather and electricity demand data together with anonymized generator contingency records from the North American Electric Reliability Corporation (NERC), we develop a three-stage Bayesian probabilistic framework for estimating winter-driven generator performance. Applied to New York State (2013--2022), the framework sequentially estimates: the hourly probability of a generator contingency event, the expected net available capacity conditioned on an event occurring, and the event duration. Colder conditions and higher electricity demand are associated with higher failure probability, lower retained capacity, and longer event duration. Under the most severe observed stress conditions, estimated mean hourly event probability reaches 24\% , while expected mean net available capacity falls to 13\% of nameplate rating. Full outage events have a median duration of 12.7 hours, while partial derating event duration increases from 2.4 to 7.1 hours with capacity loss severity. The proposed framework establishes a transferable baseline that utilities with access to plant-level records can directly extend to obtain more precise reliability estimates for operational planning and resource adequacy assessment.

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