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In the Late Noachian to Early Hesperian period, rivers transported detritus from igneous source terrains to a downstream lake within Gale crater, creating a stratified stack of fluviolacustrine rocks that is currently exposed along the slopes of Mount Sharp. Controversy exists regarding the paleoclimate that supported overland flow of liquid water at Gale crater, in large part because little is known about how chemical and mineralogical paleoclimate indicators from mafic‐rock dominated source‐to‐sink systems are translated into the rock record. Here, we compile data from basaltic terrains with varying climates on Earth in order to provide a reference frame for the conditions that may have prevailed during the formation of the sedimentary strata in Gale crater, particularly focusing on the Sheepbed and Pahrump Hills members. We calculate the chemical index of alteration for weathering profiles and fluvial sediments to better constrain the relationship between climate and chemical weathering in mafic terrains, a method that best estimates the cooler limit of climate conditions averaged over time. We also compare X‐ray diffraction patterns and mineral abundances from fluvial sediments in varying terrestrial climates and martian mudstones to better understand the influence of climate on secondary mineral assemblages in basaltic terrains. We show that the geochemistry and mineralogy of most of the fine‐grained sedimentary rocks in Gale crater display first‐order similarities with sediments generated in climates that resemble those of present‐day Iceland, while other parts of the stratigraphy indicate even colder baseline climate conditions. None of the lithologies examined at Gale crater resemble fluvial sediments or weathering profiles from warm (temperate to tropical) terrestrial climates. Plain Language Summary: Ancient rivers and streams on Mars physically and chemically altered the surface, then transported and deposited sediments, resulting in sedimentary rock production in downstream basins, as we observe in the remnants of Gale crater. However, the climate that allowed surface water to flow across the martian surface for extended periods of time remains the subject of debate. The work presented here addresses the ancient climate of Gale crater by comparing the geochemistry and mineralogy of sediments and soils on Earth to those analyzed by the Curiosity rover, specifically focusing on mudstones targeted early in the rover's traverse. A chemical weathering proxy is calculated and compared to climatological and environmental variables from various places on Earth, ultimately demonstrating that temperature is the main variable driving the extent that rocks are weathered. The results of this work suggest that the paleoclimate of Gale crater was variable, with our terrestrial reference frame providing a baseline approximation of an ancient martian climate that shifted toward Icelandic‐like conditions from even more frigid temperatures over the course of sedimentation in the ancient lake. Key Points: Terrestrial sediments and weathering profiles from basaltic terrains display first‐order similarities with mudstones from Gale crater, MarsThe chemical index of alteration can be used as paleoclimate proxy and places constraints on the ancient climate of Gale crater, MarsThe paleoclimate of Gale crater, Mars, was variable and ranged from Icelandic‐like conditions to colder climates [ABSTRACT FROM AUTHOR]