A house that has a garish style and that is overly large compared to its lot size and to the surrounding houses.
Yet the newest residential rage in Dallas is the antithesis of the traditional neighborhood: the gated community. Depending on your income and level of anxiety, these private enclaves may contain golf courses, health clubs and equestrian centers, surrounded by big hair houses of indecipherable pedigree and protected round the clock by cameras and private police.
David Dillon, "Where we live: Dallas' neighborhoods," The Dallas Morning News, May 2, 1999
When you ask [Dolly Parton] why she appeals to such a wide audience, you can tell she's given it a lot of thought by the way she unhesitatingly launches into a list of the reasons. Children like her, she believes, because, 'I look like a fairy tale, I look like Cinderella. As a little kid I was always fascinated with people that wore jewelry, long fingernails, big hair, "cause in a little kid's mind that's the way you're supposed to look, that's glamorous, that's a movie star."
Susan Wood, "Singer, Songwriter, Superstar, and still the nicest person in show business," The Washington Post, August 13, 1978
Today's phrase (spied, with thanks, by subscriber Ginna Kingsley) is a mostly Texan phenomenon, although I've spotted it in papers that originate outside of the Lone Star State. The earliest citation I could find was from the August 13, 1995 edition of The Dallas Morning News that referred to an architectural style called the "North Dallas Big Hair House."
Texas, of course, is the home of all things big, including big hair. The latter refers to a bouffant hairstyle, especially one in which long hair has been sprayed, permed, or teased to make it stand away from the head and give it volume. It was once seen as an emblem of rich, powerful, or glamorous women, but is now mocked as being garish and very "1980s."