Robert Winsor was born in Salem, Massachusetts to Dr. Frederick Winsor, a Civil War surgeon descended from renowned shipbuilder Samuel Winsor, an early settler of Duxbury, Massachusetts, and teacher Ann Bent Ware, daughter of well-known Unitarian minister, professor and abolitionist Henry Ware, Jr. .
Robert Winsor grew up in a home that doubled as his mother's school, and was later educated at Phillips Exeter Academy, graduating from Harvard University in 1880.