Tractor square dances always feature eight riders in their performances – four couples to make up the dance’s traditional 'square' — who often dress in exaggerated drag to play the male and female roles. Another important similarity between troupes is the colorful rhyming instructions of their caller, referred to as patter-call.
The video accompanying the article features the legendary Farmall Promenade troupe from Nemaha, Iowa; the actual tractor dance starts about the 20-minute mark.
A quick Google search shows what I somehow missed: plenty of tractor dancing, Ohio style: "we know it's summer when the tractors come out dancing!" --Barbara Bedway