A snow ski assembly is provided for use by an individual to slide across a snow covered surface, for example, under the force of gravity. The assembly includes a ski having a bottom wall for engaging a snow covered surface and an upturned peripheral region extending around a perimeter of the bottom wall to help facilitate sliding movement of the ski across a snow covered surface in any direction, without preference to a particular direction, and to help inhibit the ski from digging into the snow covered surface when sliding across the snow covered surface. The assembly also includes a mounting feature for coupling a binding to the bottom wall of the ski, such that an individual can position a foot in the binding and use the ski to slide across the snow covered surface.