This study develops a SARIMAX-based prediction system for short-term power outage forecasting during extreme weather events. Using hourly data from Michigan counties with outage counts and comprehensive weather features, we implement a systematic two-stage feature engineering pipeline: data cleaning to remove zero-variance and unknown features, followed by correlation-based filtering to eliminate highly correlated predictors. The selected features are augmented with temporal embeddings, multi-scale lag features, and weather variables with their corresponding lags as exogenous inputs to the SARIMAX model. To address data irregularity and numerical instability, we apply standardization and implement a hierarchical fitting strategy with sequential optimization methods, automatic downgrading to ARIMA when convergence fails, and historical mean-based fallback predictions as a final safeguard. The model is optimized separately for short-term (24 hours) and medium-term (48 hours) forecast horizons using RMSE as the evaluation metric. Our approach achieves an RMSE of 177.2, representing an 8.4\% improvement over the baseline method (RMSE = 193.4), thereby validating the effectiveness of our feature engineering and robust optimization strategy for extreme weather-related outage prediction.