When contributions from the interfacial energy become significant and comparable to the bulk energy, liquid and crystalline phases can coexist at a temperature much lower than the usual melting point. A formalism for this coexistence is given, and thermodynamic conditions for the melting of nanometer-size cubic ice crystals are derived when both the ice and water are at an equilibrium vapor pressure. By using the approximate values of surface energy and the enthalpy and entropy of melting, it is shown that nanometer-size water droplets can coexist with cubic ice particles of about the same size at temperatures in the 150-180 K range. The unusually large decrease in the temperature of a liquid-solid phase equilibrium is expected to be a general phenomenon in the nanometer-size films, clusters, and particles of materials.