A habitable planet is usually defined as one that can support liquid water on its surface. The surface temperature depends on the insolation and the greenhouse effect, caused mainly by CO2 and water vapor. The CO2 level is increased by volcanic outgassing, and decreased by continental and seafloor weathering. Here, I look at the climate evolution of Earth-like planets using a globally averaged climate model with both weathering types. Climate is sensitive to the relative strength of continental and seafloor weathering, and also the dependence of seafloor weathering on the CO2 partial pressure. Earth-like planets have two equilibrium climate states: (i) an ice-free state where outgassing is balanced by both weathering types, and (ii) an ice-covered state where outgassing is balanced by seafloor weathering only. The second of these has not been explored in detail before. For some planets, both equilibria exist, and the climate depends on the initial conditions. Insolation increases with time due to stellar evolution, so a planet usually encounters the ice-covered equilibrium first. Such a planet should remain ice-covered, even if the ice-free state appears subsequently. The ice-covered equilibrium state covers a large fraction of phase space for Earth-like planets, which implies that many planets in the conventional habitable zone may uninhabitable as a result.