In New Hampshire, to be convicted of dwi the prosecutor must show you were on a public way (usually a road), operating a motor vehicle (car, atv. etc.) and that you were under the influence or above the legal limit. Some states do not have all of these requirements. In Colorado, someone was charged while riding a horse.
http://www.foxnews.com/us/2013/09/10/colorado-man-accused-drunken-horseback-ride/?goback=.gde_1642217_member_272574964#!
"University of Colorado police have arrested a 45-year-old man suspected
of going on a drunken horseback ride through the city of Boulder.
Police say he had a small pug named Bufford in his backpack, as well as
beer cans and a black-powder pistol in his saddlebag. Officers say he
told them he was traveling from Larkspur, Colo., to his brother's
wedding in Bryce, Utah, and that he had to make the 600-mile journey by
horse because he lost his driver's license."
In Pennsylvania, someone was charged with DWI on a riding lawn mower.
http://news.findlaw.com/ap_stories/other/features/1120/09-19-2013/20130919070501_13.html?DCMP=NWL-cons_legalgrounds
"A western Pennsylvania man has been charged with driving drunk while carrying an open can of beer - on a riding lawn mower." "Police say Marrone smelled of alcohol and had an open can of Coors Light
beer in the mower's storage compartment. They say he told them he was
driving to his Murrysville home - some 6.4 miles away."