Surface liquid water is essential for standard planetary habitability. Calculations of atmospheric circulation on tidally locked planets around M stars suggest that this peculiar orbital configuration lends itself to the trapping of large amounts of water in kilometers-thick ice on the night side, potentially removing all liquid water from the day side where photosynthesis is possible. We study this problem using a global climate model including coupled atmosphere, ocean, land, and sea ice components as well as a continental ice sheet model driven by the climate model output. For a waterworld, we find that surface winds transport sea ice toward the day side and the ocean carries heat toward the night side. As a result, nightside sea ice remains