Wheeler County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 5,410. Its county seat is Wheeler. The county was formed in 1876 and organized in 1879. It is named for Royal Tyler Wheeler, a chief justice of the Texas Supreme Court.Wheeler County was one of thirty prohibition or entirely dry counties in the state of Texas. However, in approximately 2010, the community of Shamrock, located in Wheeler County at the intersection of Interstate 40 (old U.S.