Whether or not a course is closed in the winter depends on climate. Mostly courses in the western/southern US stay open, whereas mountain/snowy/cold climates are closed. Best thing to do is call your local clubs and see if they are open. Even if they are, most of the time they won't be hiring for any positions during the winter, due to less people playing, bad weather, and less daylight. We cut back on hours quite a bit at my course, and I live in CA. We don't even talk about hiring anyone until springtime.