Snow on Antarctic sea ice strongly influences the thermodynamics and freshwater balance of the coupled sea ice–upper ocean system. Yet understanding of its temporal and spatial variations remains limited by sparse observations, large uncertainties in remote sensing retrievals, and idealized model representations. We introduce a new open-source numerical model, the University of Washington Snow on Antarctic Ice Lagrangian (WASSAIL) model, that simulates the mass and bulk density evolution of snow on sea ice in the Southern Ocean over 2003–2025. Hourly reanalysis snowfall is accumulated along Lagrangian sea ice drift trajectories determined from remotely sensed ice motion fields. The single-layer model incorporates physically and empirically informed parameterizations of key erosion and transformation processes, including surface and wind-blown snow sublimation, lead trapping, rain- and non-rain-related melt, compaction from wind and overburden pressure, and the large-scale effects of sea ice convergence and divergence. Model parameters are calibrated using snow buoy measurements from the Weddell Sea. The resulting reconstruction indicates that over one-third of annual snowfall intercepted by Antarctic sea ice is lost to the atmosphere, ocean, or to melt processes prior to complete sea ice melt, with blowing snow sublimation as the dominant sink. Comparison with satellite snow depth retrievals further suggests that widespread snow-ice formation consumes 49–60 % of the remaining snow. Overall, we infer an annual meteoric freshwater input to the Southern Ocean originating from snow on sea ice of 237 mSv, equivalent to more than half of the freshwater flux associated with circumpolar sea ice melt.