The commercial pilot landed his wheel/ski equipped airplane on a frozen river. The pilot stated that after landing, he added power in an attempt to lift the tail, and turn the airplane in the opposite direction. The airplane's skis became stuck in grooves on the snow, and directional control was lost. The airplane's left wing struck a tree on the river bank and substantial damage was sustained to the leading edge. Wind conditions at the time of the accident were reported by the pilot to be calm.