If you were a child growing up in the 1960s (or even the 1970s) and told someone your last name was Woolverton, it was pretty difficult to escape the inevitable response of "oh, like the song." If you were extremely unlucky you would have been treated to a cringe-worthy rendition of either Claude King's or Johnny Horton's version's of the song following that.
Merle Kilgore and Claude King co-wrote the song, and Claude's recording was released in March, 1962. Woolverton Mountain (note the spelling) is a real place in Conway County, Arkansas. Descendants of the family still live in the area, and there are a number of ancestors buried in the Woolverton Mountain Cemetery at the top of what is actually a reasonably large hill. Clifton Taylor Clowers was a real person who lived on the mountain, and actually had two daughters (Virginia and Burlene). He died in 1994 at the age of 102. He was also Merle Kilgore's uncle, which makes the content of the song rather ironic.
In August 1962, Jo Ann Campbell released a "reply" song called "I'm the Girl from Wolverton Mountain."
Here is a YouTube version of Wolverton Mountain by Claude King.
There are a number of other locations called Woolverton Mountain (including the banner photo at the top of the page) or Wolverton Mountain around North America. They range from small to relatively large hills - the term "mountain" can be a bit subjective.