Windstorms associated with low‐pressure systems from the North Atlantic are the most important natural hazards for central Europe. Although their predictability has generally improved over the last decades, forecasting wind gusts is still challenging, due to the multiple scales involved. One of the first ensemble prediction systems at convection‐permitting resolution, COSMO‐DE‐EPS, offers a novel 2.8‐km dataset over Germany for the 2011–2016 period. The high resolution allows representation of mesoscale features that are barely captured by global models, while the long period allows both investigation of rare storms and application of statistical post‐processing. Ensemble model output statistics based on a truncated logistic distribution substantially improve forecasts of wind gusts in the whole dataset. However, some winter storms exhibit uncharacteristic forecast errors that cannot be reduced by post‐processing. During the passage of the most severe storm, gusts related to a cold jet are predicted relatively well at the time of maximum intensity, whereas those related to a warm jet are poorly predicted at an early phase. Wind gust ... mehrs are overestimated during two cases of frontal convection, which suggests that even higher resolution is needed to resolve fully the downward mixing of momentum and the stabilization resulting from convective dynamics. In contrast, extreme gusts are underestimated during a rare case involving a possible sting jet, but this arises from the representation of the synoptic rather than the mesoscale. The synoptic scale also controls the ensemble spread, which is inherited mostly from the initial and boundary conditions. This is unsurprising, but leads to high forecast uncertainty in the case of a small, fast‐moving cyclone crossing the model domain. These results illustrate how statistical post‐processing can help identify the limits of predictability across scales in convection‐permitting ensemble forecasts. They may guide the development of regime‐dependent statistical methods to improve forecasts of wind gusts in winter storms further.