After reviewing our knowledge about the presence of water on Mars and the potential advances that can be expected from the projects under development, we estimate the mission profile and potential targets of a future long-range surface vehicle. Liquid water can be detected by electromagnetic techniques through its high dielectric constant and electrical conductivity, and cold ice can be identified without ambiguity through the variations of its permittivity versus frequency at a fixed temperature. We assume a superficial layer of 1--2 m of dry, nonconductive, regolith covering a half-space mixture containing 20% of ice as a model of the subsurface at middle to moderately high latitudes. We show that a linear Wenner mutual impedance array of ~6 m, trailed behind a vehicle should detect the presence of ice at a commensurate depth. We find that the optimal frequency range is centered around 2--20 Hz at ~190 K. We discuss the synergy of these measurements with those of the ground-penetrating radar technique, which can reach larger depths. We also simulate the performance of an array accommodated on a drill or a penetrator.