Originally this referred to the reins of four horses pulling
a coach. Then it was transferred,perhaps humorously, to the original bow-tie, I believe. Correction welcomed.
O.Henry is describing attire of a bum hoping to get arrested and sent to jail to have warm winter quarters.

"Soapy had confidence in himself from the lowest button of his vest upward. He was shaven, and his coat was decent and his neat black, ready-tied four-in-hand had been presented to him by a lady missionary on Thanksgiving Day. "