What exactly does "surrey" mean, anyway?
surrey: "two-seated, four-wheeled pleasure carriage," 1895, from Surrey cart, an English pleasure cart (introduced in U.S. 1872), named for Surrey, England, where it was first made. The place name is O.E. su₫rige (722), lit. "Southerly District" (relative to Middlesex).
Maybe in the song they were riding in a carriage to a Stone Soul Picnic??