The scientific community has developed a keen interest in the processes driving the hydrologic cycle in alpine regions. The concern mainly stems from the vulnerability of snow-covered environments to the warming temperatures, such that entire ecological and social systems are at stake. Snow and ice storages in alpine regions are, in fact, fundamental water resources for large and dry lowland areas of western Americas, central Asia, northern India, and southern Europe. Snowmelt is also the principal control on the hydrologic and thermal regimes of alpine streams, which act as ecological corridors for a wide range of aquatic species. Despite the growing body of literature on the subject, the dynamics of some relevant processes are still unclear. Here, we aim at providing a deeper insight into the preferential deposition of snowfall, the wind-driven erosion and redistribution of snow, the fragmentation of drifting snow crystals, the stream temperature dynamics, and the effects of the solar radiation pattern on the hydrologic response of alpine catchments. We address our scientific questions with theoretical and numerical models that cast the complex transport phenomena in stochastic frameworks. The first part of this thesis focuses on snow transport. We combine a Lagrangian-stochastic model of particle dynamics, large-eddy simulations, and an immersed boundary method to investigate the processes driving the heterogeneous snow distribution in alpine terrain. Our results suggest that near-surface flow-particle interactions reduce snowfall deposition on the wind- and leeward slopes of the mountains, while a larger amount of snow accumulates on the hilltop and the surrounding flat terrains. Moreover, drifting and blowing snow can significantly change the snow depth distribution by eroding the hilltop and replenishing the leeward side of the ridge. We then propose a snow crystal fragmentation theory, whose assumptions are tested with discrete element simulations, to understand the transition from the size distribution of snowflakes to that of blowing snow particles. Our findings suggest that a range of scale-invariance in the blowing-snow size distribution emerges from the fractal geometry of snow crystals. Moreover, we show that the fundamental laws of energy and momentum conservation allow us to predict the number of particles ejected upon collision of drifting grains with a snow surface, characterized by arbitrary particle size distribution and cohesion. The second part of the thesis focuses on hydrological processes in alpine catchments. We first derive a theoretical framework, based on a residence time distribution approach that describes the coupled water and energy transport processes at hillslope scale. We then account for the proposed theory in a spatially explicit hydrological model to simulate stream flow and stream temperature dynamics in alpine catchments having arbitrary degrees of geomorphological complexity. Our model results highlight that highly heterogeneous advective and non-advective energy fluxes in the stream network yield water temperatures of remarkable spatial and temporal variability. Finally, we show that the effects of different solar radiation patterns on the snow-dominated hydrologic response are scale-dependent, i.e., significant at small scales where slopes present a predominant orientation, and almost negligible for catchment sizes larger than the aspect correlation scale.