The early climate of Mars (Noachian Period, the first ~20% of its history) is thought to differ significantly from that of its more recent history (Amazonian Period, the last ~66%) which is characterized by hyperarid, hypothermal conditions that result in mean annual air temperatures (MAAT) well below 0°C, a global cryosphere, minimal melting on the ground surface, and a horizontally stratified hydrologic system. We explore the nature of the fluvial and lacustrine environments in the Mars-like hyperarid, hypothermal McMurdo Dry Valleys (MDV), where the MAAT is well below 0°C (~ -14 to -30°C) in order to assess whether the Late Noachian geologic record can be explained by a climate characterized by “cold and icy” conditions. We find that the MDV hydrological system and cycle provide important insights into the potential configuration of a “cold and icy” early Mars climate in which MDV-like ephemeral streams and rivers, and both closed-basin and open-basin lakes could form. We review a series of MDV fluvial and lacustrine features to guide investigators in the analysis of the geomorphology of early Mars and we outline a new model for the nature and evolution of a “cold and icy” Late Noachian climate based on these observations. We conclude that a cold and icy Late Noachian Mars with MAAT below freezing, but peak seasonal and peak daily temperatures above 0°C, could plausibly account for the array of Noachian-aged fluvial and lacustrine features observed on Mars. Our assessment also provides insight into the potential effects of punctuated warming on a cold and icy early Mars, in which impact crater formation or massive volcanic eruptions cause temperatures in the melting range for decadal to centennial timescales. We outline a set of outstanding questions and tests concerning the nature and evolution of these features on Mars.