Although the melting of ice is the most ubiquitous phase transition, (pre)melting and the quasi-liquid layer remain a matter of debate, and little is known about the relationship between the thermodynamic properties of ice nanocrystals and their size and dimensionality. Here, we model analytically the size- and dimensionality-dependent melting temperature, premelting temperature, and melting enthalpy of hydrogen-bonded ice nanocrystals. These three thermodynamic parameters are found to increase with increasing size and dimensionality where the size effect is principle while the dimensionality effect is secondary, and the size dependence of premelting temperature almost follows the same trend as that of melting temperature. The model predictions correspond to the available molecular dynamic simulation and experimental results of ice nanoparticles and nanowires. These agreements enable us to determine theoretically the thickness of the quasi-liquid layer for the first time, which is found to be not constant but slightly increase with increasing size and thus accounts for the occurrence of different reported thicknesses of the quasi-liquid layer.