Understanding spin orbital parameter-driven climate change on Mars prior to ∼ 20 Ma ago requires geological evidence because numerical solutions for that period are chaotic and non-unique. We show geological evidence that lineated valley fill at low mid-latitudes in the northern hemisphere of Mars (∼ 37.5° N) originated through regional snow and ice accumulation and underwent glacial-like flow. Breached upland craters and theater-headed valleys reveal features typical of erosion in association with terrestrial glaciers. Parallel, converging and chevron-like lineations in potentially ice-rich deposits on valley floors indicate that flow occurred through constrictions and converged from different directions at different velocities. Together, these Martian deposits and erosional landforms resemble those of intermontaine glacial systems on Earth, particularly in their major morphology, topographic shape, planform and detailed surface features. An inferred Late Amazonian age, combined with predictions of climate models, suggest that the obliquity of Mars exceeded a mean of 45° for a sustained period. During this time, significant transfer of ice occurred from ice-rich regions (e.g., the poles) to mid-latitudes, causing prolonged snow and ice accumulation there and forming an extensive system of valley glaciers.