Moore is an unincorporated community and census-designated place in Frio County, Texas, United States. Its population was 610 at the 2020 census. Moore is located in northeastern Frio County. Interstate 35 passes through the community, with access from Exit 114. I-35 leads northeast 44 mi to downtown San Antonio and southwest 13 mi to Pearsall, the Friā¦Moore is an unincorporated community and census-designated place in Frio County, Texas, United States. Its population was 610 at the 2020 census. Moore is located in northeastern Frio County. Interstate 35 passes through the community, with access from Exit 114. I-35 leads northeast 44 mi to downtown San Antonio and southwest 13 mi to Pearsall, the Frio County seat.