Grey Fox is open all winter. Red Fox also just got a complete redesign with short (concrete) and long (mulch) tees. Dretzka Park in Milwaukee is rearranged to a shorter winter layout, but is playable. Brown Deer is pulled over winter. I'm not sure about Kenosha (UW Parkside), someone may have to chime in on that one. They either pull the baskets for the winter or just during muddy season in spring.
Courses in Illinois (except Palatine) stay in all winter.