At a given thermodynamic condition, nucleation events occur at a frequency that scales with the volume of the system. Therefore at the nanoscale, one may expect to obtain supercooled liquids below the bulk homogeneous nucleation temperature. Here we report direct computational evidence that in supercooled water nano-droplets ice nucleation rates are strongly size dependent and at the nanoscale they are several orders of magnitude smaller than in bulk water. Using a thermodynamic model based on classical nucleation theory, we show that the Laplace pressure is partially responsible for the suppression of ice crystallization. Our simulations show that the nucleation rates found for droplets are similar to those of liquid water subject to a pressure of the order of the Laplace pressure within droplets. Our findings aid the interpretation of molecular beam experiments and support the hypothesis of surface crystallization of ice in microscopic water droplets in clouds.