In this study we construct and compare three different deep learning (DL) models for estimating daily snow water equivalent (SWE) from high-resolution gridded meteorological fields over the Rocky Mountain region. Snow Telemetry (SNOTEL) station based observations are used as the prediction target. All DL models produce higher median Nash-Sutcliffe Efficiency (NSE) values than an analogous process-based product, although their mean squared errors also tend to be higher. Sensitivity of the SWE prediction to the model’s input variables is analyzed using an explainable artificial intelligence (XAI) method, yielding insight into the physical relationships learned by the models. As expected, this method reveals the dominant role precipitation and temperature play in snowpack dynamics. In applying our models to estimate SWE throughout the Rocky Mountains, an extrapolation problem arises since the statistical properties of SWE (e.g., annual maximum) and geographical properties of individual grid points (e.g., elevation) differ from the training data. This problem is solved by switching the prediction target for all tested DL models. Finally the spatial and temporal responses of SWE with respect to climate change is investigated with forcings from down-scaled Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations. The projection results show a substantial decrease in both maximum SWE and snow season length over the lower elevation areas. Our work shows that the DL models are promising tools for estimating SWE, and sufficiently capture relevant physical relationships to make them useful for spatial and temporal extrapolation of SWE values.