Hydrothermal spring systems may well have been present on early Mars and could have served as a habitat for primitive life. The integrated instrument suite of the Athena Rover has, as a component on the robotic arm, a Mossbauer spectrometer. In the context of future Mars exploration we present results of Mossbauer analysis of a suite of samples from an iron-rich thermal spring in the Chocolate Pots area of Yellowstone National Park (YNP) and from Obsidian Pool (YNP) and Manitou Springs, Colorado. We have found that Mossbauer spectroscopy can discriminate among the iron-bearing minerals in our samples. Those near the vent and on the surface are identified as ferrihydrite, an amorphous ferric mineraloid. Subsurface samples, collected from cores, which are likely to have undergone inorganic and/or biologically mediated alteration (diagenesis), exhibit spectral signatures that include nontronite (a smectite clay), hematite (alpha-Fe2O3), small-particle/nanophase goethite (alpha-FeOOH), and siderite (FeCO3). We find for iron minerals that Mossbauer spectroscopy is at least as efficient in identification as X-ray diffraction. This observation is important from an exploration standpoint. As a planetary surface instrument, Mossbauer spectroscopy can yield high-quality spectral data without sample preparation (backscatter mode). We have also used field emission scanning electron microscopy (FESEM), in conjunction with energy-dispersive X ray (EDX) fluorescence spectroscopy, to characterize the microbiological component of surface sinters and the relation between the microbiological and the mineralogical framework. Evidence is presented that the minerals found in these deposits can have multi-billion-year residence times and thus may have survived their possible production in a putative early Martian hot spring up to the present day. Examples include the nanophase property and the Mossbauer signature for siderite, which has been identified in a 2.09-billion-year old hematite-rich chert stromatolite. Our research demonstrates that in situ Mossbauer spectroscopy can help determine whether hydrothermal mineral deposits exist on Mars, which is significant for exobiology because of the issue of whether that world ever had conditions conductive to the origin of life. As a useful tool for selection of samples suitable for transport to Earth, Mossbauer spectroscopy will not only serve geological interests but will also have potential for exopaleontology.