Any study of water behavior in the Martian regolith should begin with an examination of our current understanding of subsurface water in terrestrial cold regions. The terrestrial analog provides a wealth of readily available information to help formulate and test new ideas about possibilities on Mars. This paper discusses the major mechanisms driving the phenomenal ability of capillary media to redistribute moisture when freezing. It examines both thermally induced and freezing-induced redistribution of moisture, the magnitude of which can vastly exceed the transport expected from Fickian diffusion alone. If the Martian crust is truly water-rich, then these processes (in response to transient thermal disturbances caused by impacts, volcanic and magmatic activity, changes in climate, and potential future human activities) may induce substantial changes in the local distribution of subsurface ice.