The growth of ice nuclei through deposition of water vapor at temperatures below frost point is investigated in the context of the Antarctic winter stratosphere. The altitude and the ambient water vapor mixing ratio, as well as the size of the nuclei determine the ice particle growth rate, with higher altitudes requiring colder temperatures for ice deposition. The magnitude of the temperature decrease below the frost point and its evolution over the winter determine the residence time of the growing ice particles and the loss of water vapor at any altitude. A winter-long simulation, using the observed South Pole daily temperatures, suggests that, in the limit of weak latitudinal mixing over the austral winter, considerable dehydration can occur within the polar vortex, with the higher altitudes (above 22 km.) experiencing the least losses.