We present a molecular dynamics study of ice growth from supercooled water. By performing a series of simulations with different initial conditions, we have quantitative established the relationship existing between the critical nucleus size and the temperature. The results show that ice embryos containing hundreds or thousands of molecules are needed for the system to crystallize macroscopically, even at high degrees of supercooling. Our findings explain the difficulty in observing spontaneous ice nucleation in atomistic simulations and the relative ease with which water droplets can be supercooled under controlled experiments.