The ice isn't to cool the water, the ice is to reflect most of the incoming light.

Sea ice keeps the polar regions cool and helps moderate global climate. Sea ice has a much brighter surface compared to many other Earth surfaces, particularly the surrounding ocean. The darker ocean reflects only 6 percent of the sun’s energy and absorbs the rest, while sea ice reflects 50 to 70 percent of the incoming energy.

-- https://nsidc.org/learn/parts-cryosphere/sea-ice/quick-facts-about-sea-ice