It is illegal to drive without windshield wipers. You don’t need a windshield, but you must have the wipers.

Sec. 39-13. Pedestrians, bicycles, etc., prohibited on certain interstate highways. It shall be unlawful and an offense against the city for pedestrians to be upon, or for any person to operate a bicycle, a nonmotorized vehicle or a motor driven cycle of less than ten (10) horsepower, on any part of Interstate Highway 10 and…