This document is the final report of the Ice and Climate Evolution Science Analysis Group (ICESAG) that was formed by the Mars Exploration Program Analysis Group (MEPAG) as part of its preparations for the upcoming NASA Planetary Science Decadal Survey for 2023 through 2032 (see §1). Through telecons, one face-to-face meeting, and discussions with experts in relevant topics, ICE-SAG has identified high-priority science questions and key measurements that are needed to address them as well as the 2018 MEPAG Goals and the 2013-2022 NASA Planetary Science Decadal Survey goals [V&V, 2011] pertaining to ice1 and climate. Obtaining these measurements would yield dramatic improvements in our understanding of the climate history of Mars, which is critical to investigations of Martian geologic history and habitability and will also inform the potential of buried water ices as in situ resources for future human missions. In many ways, the Martian climate system serves as a laboratory for a broader understanding of planetary climate systems including the Earth’s, which is substantially more complex due to a denser atmosphere, a more active planetary interior, and interactions with oceans and abundant life, while operating under much more subtle orbital forcing. Thus, advancements in Martian climate science will have far-reaching impacts that extend to studies of the Earth and other planetary bodies.