Molecular mechanisms of the electric polarization of supercooled water at its interface with the basal face of β-AgI crystal are studied by computer simulation. By the background of thermal fluctuations at 260 K, the gradual growth of the molecular film from vapor is reproduced from the submonomolecular stage to the bulk liquid and the mechanism of electric double layer formation is analyzed in detail. Polarization of the contact layer of water is caused by the local fields at its interface with the crystal surface. The potential difference in the electric double layer emerging on the basal face of the single crystal reaches 0.88 V but is different on different faces as regards both its magnitude and sign. The asymmetry in the spatial charge distribution in the H2O molecule is responsible for the different strength of water adhesion to the surface of crystal faces containing either positive or negative ions in their crystallographic surface layer. In an aqueous electrolyte containing ionic impurities, the electric double layer field induces compensating motion of mobile charge carriers to the crystal surface and their adsorption. As a result of contact-layer polarization, a micro-crystal immersed into an electrolyte droplet exerts the distilling effect on the latter, and the adsorption of mobile ions on the surface of a solid-crystalline particle can affect its activity as the center of heterogeneous nucleation of atmospheric moisture.