Snow distribution over sea ice is an important control on sea ice physical and biological processes. We combine measurements of the atmospheric boundary layer and blowing snow on an Antarctic sea ice floe with terrestrial laser scanning to characterize a typical storm and its influence on the spatial patterns of snow distribution at resolutions of 1–10 cm over an area of 100 m × 100 m. The pre‐storm surface exhibits multidirectional elongated snow dunes formed behind aerodynamic obstacles. Newly deposited dunes are elongated parallel to the predominant wind direction during the storm. Snow erosion and deposition occur over 62% and 38% of the area, respectively. Snow deposition volume is more than twice that of erosion (351 m3 versus 158 m3), resulting in a modest increase of 2 ± 1 cm in mean snow depth, indicating a small net mass gain despite large mass relocation. Despite significant local snow depth changes due to deposition and erosion, the statistical distributions of elevation and the two‐dimensional correlation functions remain similar to those of the pre‐storm surface. Pre‐storm and post‐storm surfaces also exhibit spectral power law relationships with little change in spectral exponents. These observations suggest that for sea ice floes with mature snow cover features under conditions similar to those observed in this study, spatial statistics and scaling properties of snow surface morphology may be relatively invariant. Such an observation, if confirmed for other ice types and conditions, may be a useful tool for model parameterizations of the subgrid variability of sea ice surfaces.