In this brief report we consider the possibility that the northern plains of Mars would today be a frozen ocean, covered by a rather thin (at most of the order of a few hundred meters) layer of volcanic and impact debris and dust that prevents the ice beneath from being directly observed and thermally protects it from summertime sublimation (according to current models, subsurface ice in the high latitudes is stable under current climatic conditions). The frozen ocean hypothesis would naturally explain the striking topographic flatness of the northern plains. We show that the frozen ocean is plausible in terms of current models of paleoclimatic development. We also discuss the possibility that a remnant salty brine ocean could still exist under the ice and that electric currents flowing in it would be responsible for the recently observed ~40 nT Northern Hemisphere magnetic anomalies. The latter hypothesis could be tested by suitably placed surface magnetometers.