Willow Park is a city in Parker County, Texas, United States. The population was 4,936 in 2020. Willow Park was the location of Trinity …Willow Park is a city in Parker County, Texas, United States. The population was 4,936 in 2020. Willow Park was the location of Trinity Meadows Race Track, one of the first horse racing tracks opened once Texas legalized parimutuel betting. However, it was never seriously considered for upgrade to first-class status, and once Lone Star Park opened, Trinity Meadows Race Track closed. It is home to Squaw Creek golf course, located just off Ranch House Road.