Friona is a city in Parmer County, Texas, United States. The population was 4,171 at the 2020 census. Friona was established as a small co…Friona is a city in Parmer County, Texas, United States. The population was 4,171 at the 2020 census. Friona was established as a small community in 1898 by XIT Ranch, originally called Frio, which is also the word for "cold" in Spanish.