Snow falling uniformly on a distribution of ice thicknesses results in a distribution of snow-cover thicknesses. These snow depths depend on the amount of snow fall, the time of year at which it falls, and the thickness of the underlying ice. The effect of snowfall on snow-ice-thickness distribution is examined using a single-column ice-ocean model. The time at which snow begins to accumulate, and melt ponds and leads freeze, affects the surface albedo. The rate of snowfall affects ice-growth rates and, as a result, the ice-thickness distribution. During the period of rapid ice growth between the autumn freeze and mid-winter, snow falling on newly formed ice is rapidly depleted due to sublimation. Snow falling on thicker ice remains throughout the winter to create a source of meltwater for ponds and runoff into the ocean.