Can I leave butter cookies in the fridge?
I would store them outside, not inside the fridge. Fridge temperatures make anything containing flour go stale quickly. Of course, sometimes people have to live with it, such as when they have made a cake with perishable icing or filling. But cookies are not perishable, so they are better stored outside of the fridge. 

As to whether to put them in a sealed container or not, it depends on the cookie. The harder type does all right in the air, and can get flaccid in a sealed container. If they are soft, they are probably better off covered. It is still preferable to not isolate them completely, a canvas bag or a bread box with ventilation slits does better.