Chestnut Mound, TennesseeChestnut Mound is an unincorporated community in Smith County, United States. Its ZIP code is 38552.ClimateChestnut Mound's climate is four-season subtropical under Köppen, typical of Tennessee. Chestnut Mound lies in USDA Hardiness Zone 7a, so the coldest night of the year typically drops to 0 to 5 degrees Fahrenheit.