Legacy Roads and Trails Act This bill directs the Department of Agriculture (USDA) to establish the Forest Service Legacy Roads and Trails Remediation Program. Specifically, under the program, the Forest Service, taking into account predicted changes in weather and hydrology related to global climate change, shall carry out storm damage risk reduction, including deferred maintenance, repairs, road and trail relocation, and associated activities on roads, trails, tunnels, and bridges under the jurisdiction of the Forest Service; restore waterways and natural migration of fish and other aquatic species by removing or replacing culverts or other infrastructure from such waterways; and decommission unneeded roads. In implementing the program, the Forest Service shall give priority to projects that protect or restore water quality and watershed function; a watershed that supplies a public drinking water system; the habitat of a threatened, endangered, or sensitive fish or wildlife species, or a species of conservation concern; or a watershed for which the Forest Service has completed a watershed protection and restoration action plan. The Forest Service shall identify the minimum road system needed for each unit of the National Forest System. USDA shall review, and may revise, an identification of the minimum road system in accordance with federal regulations relating to the administration of the forest transportation system.