Weather variables are an important driver of power generation from renewable energy sources. However, accurately predicting such variables is a challenging task, which has a significant impact on the accuracy of the power generation forecasts. In this study, we explore the impact of imperfect weather forecasts on two classes of forecasting methods (statistical and machine learning) for the case of wind power generation. We perform a stress test analysis to measure the robustness of different methods on the imperfect weather input, focusing on both the point forecasts and the 95% prediction intervals. The results indicate that different methods should be considered according to the uncertainty characterizing the weather forecasts.