By shifting winter precipitation into summer freshet, the cryosphere supports life across the world. The sensitivity of this mechanism to climate and the role played by the cryosphere in the Earth's energy budget have motivated the development of a broad spectrum of predictive models. Such models represent seasonal snow and glaciers with various complexities and generally are not integrated with hydrologic models describing the fate of meltwater through the hydrologic budget. We present Snow Multidata Mapping and Modeling (S3M) v5.1, a spatially explicit and hydrology-oriented cryospheric model that simulates seasonal snow and glacier evolution through time and that can be natively coupled with distributed hydrologic models. Model physics include precipitation-phase partitioning, snow and glacier mass balances, snow rheology and hydraulics, a hybrid temperature-index and radiation-driven melt parametrization, and a data-assimilation protocol. Comparatively novel aspects of S3M are an explicit representation of the spatial patterns of snow liquid-water content, the implementation of the Δh parametrization for distributed ice-thickness change, and the inclusion of a distributed debris-driven melt factor. Focusing on its operational implementation in the northwestern Italian Alps, we show that S3M provides robust predictions of the snow and glacier mass balances at multiple scales, thus delivering the necessary information to support real-world hydrologic operations. S3M is well suited for both operational flood forecasting and basic research, including future scenarios of the fate of the cryosphere and water supply in a warming climate. The model is open source, and the paper comprises a user manual as well as resources to prepare input data and set up computational environments and libraries.