A continuous time process of alternating stochastic growths and deterministic decays is proposed as a simple model for the interannual dynamics of snow water equivalent (SWE) storage and melting. The related stationary properties are studied, and an integral difference equation for the probability density function of the state variable is derived. The corresponding solution is obtained by both solving the master equation numerically and simulating the process with a Monte Carlo scheme. An analytical solution is also obtained for the inverse problem, i.e., when the pdf of growths that lead to accumulation is reconstructed from that of the process. The model's statistical properties help explain the probabilistic character of the end of summer snowlines and their intrinsic variability with the geographic location and climatic factors. Possible applications to model the interannual SWE cover evolution or to reconstruct the past precipitation characteristics are also discussed.