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

Sec. 15-1. Motor vehicles restricted. No motorized vehicles of any type shall be allowed on public parks, playgrounds, or school areas under the supervision of the department of parks and recreation unless the person operating such vehicle shall have first received written permission from the director of parks and recreation, with the exception of motorized…