The availability of water-ice at the surface in the Mars polar cap and within the top meter of the high-latitude regolith raises the question of whether liquid water can exist there under some circumstances and possibly support the existence of biota. We examine the minimum temperatures at which liquid water can exist at ice grain-dust grain and ice grain-ice grain contacts, the minimum subfreezing temperatures at which terrestrial organisms can grow or multiply, and the maximum temperatures that can occur in martian high-latitude and polar regions, to see if there is overlap. Liquid water can exist at grain contacts above about -20 degrees C. Measurements of growth in organisms isolated from Siberian permafrost indicate growth at -10 degrees C and metabolism at -20 degrees C. Mars polar and high-latitude temperatures rise above -20 degrees C at obliquities greater than ~40 degrees, and under some conditions rise above 0 degrees C. Thus, the environment in the Mars polar regions has overlapped habitable conditions within relatively recent epochs, and Mars appears to be on the edge of being habitable at present. The easy accessibility of the polar surface layer relative to the deep subsurface make these viable locations to search for evidence of life.