There are 2 US Post Offices in Winkler County serving a total of 7,099 residents equating to 3,550 residents per post office. It's estimated that approximately 11,331 packages are handled across the 2 county post offices annually. Winkler County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 7,110. Its county seat is Kermit. The county was created in 1887 and organized in 1910. It is named for Clinton M. Winkler, a Colonel in the Confederate Army. Part of the large Haley Ranch, founded by the father of Texas historian J. Evetts Haley, is in Winkler County, with another portion in neighboring Loving County."