Mars exploration is focused on seeking evidence of habitable environments and microbial life. Terrestrial glassy basalts may be the closest Mars‐surface weathering analog and observations increasingly indicate their potential to preserve biogeochemical records. The textures, major and trace element geochemistry, and N concentrations and isotopic compositions of subaerial, subglacial and continental lacustrine hyaloclastites from Antarctica, Iceland, and Oregon, respectively, were studied using micro‐imaging and chemical methods, including gas‐source mass spectrometry. Alteration by meteoric‐sourced waters occurred in circum‐neutral, increasingly alkaline low‐temperature conditions of ∼60°C–100°C (Iceland) and ∼60°C–170°C (Antarctica). Incompatible large ion lithophile element (LILE) enrichments compared to mid‐ocean ridge basalt (MORB) are consistent with more advanced alteration in Antarctic breccias consisting of heulandite‐clinoptilolite, calcite, erionite, quartz, and fluorapophyllite. Granular and tubular alteration textures and radial apatite represent possible microbial traces. Most samples contain more N than fresh MORB or ocean island basalt reflecting enrichment beyond concentrations attributable to igneous processes. Antarctic samples contain 52–1,143 ppm N and have δ15Νair values of −20.8‰ to −7.1‰. Iceland‐Oregon basalts contain 1.6–172 ppm N with δ15Ν of −6.7‰ to +7.3‰. Correlations between alteration extents, N concentrations, and concentrations of K2O, other LILEs, and Li and B, reflect the siting of secondary N likely as NH4+ replacing K+ and potentially as N2 in phyllosilicates and zeolites. Although much of the N enrichment and isotope fractionation presented here is not definitively biogenic, given several unknown factors, we suggest that a combination of textures, major and trace element alteration and N and other isotope geochemical compositions could constitute a compelling biosignature in samples from Mars' surface/near‐surface.