After Joe and Connie Mitchell’s son and his bride said their vows beneath an arbor of gnarled cedar trees on the family ranch near Glen Rose, Texas, it was time to celebrate—so everyone headed for the party barn.

There, under hand-hewn hemlock rafters strung with lights and decked with greenery, more than 200 wedding guests dined on Tex-Mex and danced to an eight-piece band, crowding a dance floor that was buried under hay a century ago.

...