Closson was born in Thetford, Vermont in 1848. His father served as a Vermont Legislator and his mother was a painter Benjamin West. He was educated at the Thetford Academy, and upon graduation worked as a clerk in a railroad office.
Shortly thereafter, he moved to Boston Massachusetts and worked as an apprentice with a wood engraver. He studied drawing at the Lowell Institute, and began working for Harper’s Magazine as well as other publishing houses in Boston.
Seventeen of his paintings are in the American Art Collection at the Smithsonian Institution. He also has artwork on display at the Wadsworth Athenaeum in Hartford and the Cleveland Museum of Art.
He married Grace Worden Gallaudet Kendall. They moved to Hartford Connecticut where he passed away and was buried.