The Tibetan Plateau (TP) is often called the “Water Tower of Asia,” which contains the largest amount of snow and glaciers outside the polar regions. As an important and variable feature of the land surface, snow coverage on the TP has great impacts on regional climate. However, the commonly used ERA5 reanalysis in dynamical downscaling largely overestimates the snow depth for the TP. To improve the representation of snow cover in ERA5, a new ERA5‐driven downscaling data set (High Asia Refined analysis version 2, HAR v2) was generated by the Weather Research and Forecasting (WRF) model with the bias‐corrected snow depth. This study aims to identify and better understand the impact of bias‐corrected initial snow conditions on simulated regional climate, by comparing the HAR v2 with a 5‐year ERA5 forced WRF simulation without bias correction of initial snow depth (referred to as WRF_ERA5). The results show that the bias correction significantly improves the simulation of 2 m air temperature (T2), with regional mean cold bias reduced by 0.2°C–2.4°C, but no significant improvement in precipitation simulation is found. Further comparative analysis reveals that higher snow depth in WRF_ERA5 leads to T2, mean daily precipitation, summer extreme precipitation, and contributions of convective precipitation to summer mean daily precipitation decrease by 0°C–4°C, 0%–60%, 0%–40%, and 0%–10%, respectively, in most areas of the TP. In addition, the bias‐corrected initial snow depth also has impacts on simulated diurnal cycles of precipitation and T2 and leads to peak hours one hour earlier. Overall, this study confirms the importance of snow cover for the climate in the TP.