There are 1 US Post Offices in Cottle County serving a total of 1,493 residents equating to 1,493 residents per post office. It's estimated that approximately 2,383 packages are handled across the 1 county post offices annually. Cottle County is a county in the U.S. state of Texas. As of the 2010 census, its population was 1,505. Its county seat is Paducah. The county was founded in 1876 and later organized in 1892. It is named for George Washington Cottle, who died defending the Alamo. Cottle County was formerly one of 46 prohibition, or entirely dry counties in the state of Texas. It now allows beer and wine sales. The Matador Ranch, based in Motley once reached into Cottle County.