The recent development of high-resolution climate models offers a promising approach in improving the simulation of precipitation, clouds and temperature. However, higher grid spacing is also a promising feature to improve the simulation of snow cover. In particular, it provides a refined representation of topography and allows for an explicit simulation of convective precipitation processes. In this study we analyze the snow cover in a set of decade-long high-resolution climate simulation with horizontal grid spacing of 2.2 km over the greater Alpine region. Results are compared against observations and lower resolution models (12 and 50 km), which use parameterized convection. The simulations are integrated using the COSMO (Consortium for Small-Scale Modeling) model. The evaluation of snow water equivalent (SWE) in the simulation of present-day climate, driven by the ERA-Interim reanalysis, against an observational dataset, reveals that the high-resolution simulation clearly outperforms simulations with grid spacing of 12 and 50 km. The latter simulations underestimate the cumulative amount of SWE over Switzerland over the whole annual cycle by 33% (12 km simulation) and 56% (50 km simulation) while the high-resolution simulation shows a spatially and temporally averaged difference of less than 1%. Scenario simulations driven by GCM MPI-ESM-LR (2081–2090 RCP8.5 vs. 1991–2000) reveal a strong decrease of SWE over the Alps, consistent with previous studies. Previous studies had found that the relative decrease becomes gradually smaller with elevation, but this finding was limited to low and intermediate altitudes (as a 12 km simulation resolves the topography up to 2500 m). In the current study we find that the height gradient reverses sign, and relative reductions in snow cover increases above 3000 m asl, where important parts of the cryosphere are present. In addition, the simulations project a transition from permanent to seasonal snow cover at high altitudes, with potentially important impacts to Alpine permafrost. This transition and the more pronounced decline of SWE emphasize the value of the higher grid spacing. Overall, we show that high-resolution climate models offer a promising approach in improving the simulation of snow cover in Alpine terrain.