Freezing of water under nanoconfinement exhibits physical peculiarities with respect to the bulk water. However, experimental observations are extremely challenging at this scale, which limits our understanding of the effect of confinement on water properties upon freezing. In this study, we use molecular dynamic simulations to investigate how confinement affects the kinetics of growth of ice and the thermodynamic equilibrium of ice-liquid coexistence. TIP4P/Ice water model and CSH-FF model were applied to simulate ice crystallization in a confined cement system at temperatures down to 220 K. We adapted an interface detection algorithm and reparameterized the CHILL/CHILL+ algorithm to capture ice growth. The confinement leads to a shift of the maximum growth rate of ice to a higher temperature than for bulk water. Both the confinement and surface impurities contribute to slowing down the ice growth. For the ice-liquid coexistence at equilibrium, we derive a formulation of Thomson’s equation adapted to statistical physics quantities accessible by molecular simulation, and we show that this adapted equation predicts accurately the melting line of bulk and confined ice Ih as a function of pressure. The confinement decreases systematically the melting temperature of ice of about 5 K compared with bulk ice Ih. A premelted water film about 1 nm thick is observed between the solid wall and ice, and its thickness is found to decrease continuously as temperature is lowered. We note that the surface impurities are key to the formation of the premelted water nanofilm when the temperature is lower than 250 K.