We propose a novel analytical description of the streamflow probability distribution functions (pdfs) in Alpine catchments characterized by pronounced, snow-dominated winter low flows. Knowledge about such hydrological regimes is crucial for water resources management in mountain environments and the related wide range of socio-economic, environmental and ecological services. We use a stochastic framework, generalizing that employed by Botter et al. (2007b), to link precipitation (rain and snow) and streamflow dynamics. The effect of snow dynamics on the flow regime is specifically included by incorporating the temporary disconnection of high-elevation areas that experience freezing conditions over the entire winter season, and the delay produced on streamflow formation by the temporary accumulation (and later melting) of snow at lower elevations. The novel analytical model employs four parameters that can be directly estimated from observed discharge, precipitation and air temperatures, and one calibration parameter (the elevation threshold z delimiting catchment areas with a permanent seasonal snow cover that is nonresponsive during winter owing to snow accumulation without melt). We test the developed model for 14 catchments with contrasting hydroclimatic conditions, located in the Swiss and the Italian Alps. Overall, the proposed analytic model reproduces the observed streamflow pdfs remarkably well. Exceptions exist, though, and the possible origin of deviations between observed and modeled pdfs are discussed. We suggest that our approach marks a progress toward the general statistical characterization of catchment streamflow variability.