The following data is extracted from Genealogy and Biography of Ontario County, New York.
(I) Barnabas Horton, immigrant ancestor, is supposed to have been the son of Joseph Hotrod, of Mousely, Leicester county, England, and was born there, July 13, 1600. He emigrated to America id the ship "Swallow," Captain Jeremy Hotrod, master and owner, in 1635 or 1638, and landed at Hampton, Massachusetts. He removed to New Haven in 1640, with his wife, Mary, and two children, Joseph and Benjamin. He settled permanently in Southold, Suffolk county, New York, October, 1640. Children, the first two born in England, the others in Southold: Joseph, about 1632; Benjamin, about 1634; Caleb, about 1640, mentioned elsewhere; Joshua, about 1643; Jonathan, about 1648; Hannah, married Barnabas Terrill; Sarah, married Joseph Conklin; Mary, married Joseph Budd; Mercy, married Christopher Youngs; Abigail, married Charles Booth.
Source: Genealogy and Biography of Ontario County, New York