Runoff predictions are affected by several uncertainties. Among the most important ones is the uncertainty in meteorological forcing. We investigated the skill propagation of meteorological to runoff forecasts in an idealized experiment using synthetic data. Meteorological forecasts with different skill were produced with a weather generator and fed into two different hydrological models. The experiments were repeated for two glacierized catchments of different sizes and morphological characteristics, and for scenarios of different glacier coverage. The results show that for catchments with high glacierization (>50%), the runoff forecast skill is more dependent on the skill of the temperature forecasts than the one for precipitation. This is because snow and ice melt are strongly controlled by temperature. The influence of the temperature forecast skill diminishes with decreasing glacierization, while the opposite is true for precipitation. Precipitation starts to dominate the runoff skill when the catchment’s glacierization drops below 30%, or when the total contribution of ice and snow melt is less than about 60%. The skill difference between meteorological forecasts and runoff predictions proved to be independent from the lead time, and all results were similar for both the considered hydrological models. Our results indicate that long-range meteorological forecasts, which are typically more skillful in predicting temperature than precipitation, hold particular promise for applications in snow- and glacier-dominated catchments.