The extent and the morphology of ice forming in a differentially heated cavity filled with water is studied by means of experiments and numerical simulations. We show that the main mechanism responsible for the ice shaping is the existence of a cold upward convective current in the system. Such a current is ascribed to the peculiar equation of state of water, i.e., the non-monotonous dependence of density with temperature. The precise form of the ice front depends on several factors, first the temperature difference across the cell which drives the convection, second the wall inclination with respect to the vertical, both of which are here explored. We propose a boundary-layer model and a buoyancy-intensity model which account for the main features of the ice morphology.