I keep certain areas of my fellas cage and pen covered. They have cardboard boxes in the pen they can hide in, and the back half of their cage is covered.
The opposite corner of the pen is also covered, but the vast majority of it is open. Both pigs will lie in the beds that are covered, or uncovered.
Long and short of it, is that it really depends on the personality of your pig. Some pigs are much more fearful than others, which is of course because they are prey animals. My boys have come to learn that where they live is in complete safety, and they are comfortable in the cage no matter where they are. Your pigs may or may not come to understand the same.