Recent discovery of transient ice deposits uncovered by five small craters between 40 and 55°N latitude, reinterpretation of MONS neutron data that indicate the wide-spread presence of ice within 1 m of the surface at midlatitudes (down to 30°N) of Mars, and evidence of recent periglacial activity within 10°N of the equator, all suggest ice may be or recently was present at latitudes where it is not expected and at unexplained abundance. As ice may be unstable under present Mars climatic conditions, a mechanism may be needed to explain the presence of ice in the near surface at these latitudes. Water release history, chemical composition, and heat fluxes are variable over the surface of Mars, and there could be more than one mechanism responsible for near-surface ice. The purpose of this study is to show that hydrothermal circulation of brines in the subsurface of Mars is a possible mechanism that can deposit ice and brine, close to, or even at, the surface of Mars. Furthermore, the action of brine convection can be related to some of the surface features associated with subsurface water during previous or even present epochs, such as polygonal ground and sorted stone circles.