The aim of this study is to investigate the competing effects of a snow layer's insulation and snow-ice formation on thermodynamic sea ice thickness growth in response to changes in precipitation. Using optimal interpolation to assimilate Special Sensor Microwave/Imager satellite-derived snow depths into a dynamic-thermodynamic sea ice model, we create a daily assimilated snow depth product for the years 1992--2003. The assimilated snow depths are used to adjust National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis precipitation rates which subsequently force the model's snow depths and freshwater input. These adjusted precipitation rates are used to create a best estimate snow depth climatology. This climatology provides the basis for a series of sensitivity experiments. Precipitation rates are varied from 0.0 to a doubling of the present day precipitation. Initially, sea ice volume decreases with increasing precipitation rate multiplying factor (PRMF) because of the insulation effects of a deeper snow layer. The turning point at which the insulation effect becomes balanced by the snow to ice conversion effect ranges from PRMF = 0.50 to PRMF = 0.75, depending upon the snow thermal conductivity and density. This suggests that with present-day precipitation rates the snow effect on Southern Ocean sea ice is dominated by snow-ice formation rather than the snow's insulation.