Barnet is a town in Caledonia County, Vermont, United States. The population was 1,663 at the 2020 census. Barnet contains the locations of Barnet Center, East Barnet, McIndoe Falls, Mosquitoville, Passumpsic and West Barnet. The main settlement of Barnet is recorded as a census-designated place by the U.S. Census Bureau, with a population of 12…Barnet is a town in Caledonia County, Vermont, United States. The population was 1,663 at the 2020 census. Barnet contains the locations of Barnet Center, East Barnet, McIndoe Falls, Mosquitoville, Passumpsic and West Barnet. The main settlement of Barnet is recorded as a census-designated place by the U.S. Census Bureau, with a population of 127 at the 2020 census.