Consider the thong bikini. But you were asking about bridges. You realize, first of all, that covered bridges are wooden. Excuse me if I spell this out in excessive detail, but these days one can leave nothing to chance. The uninformed believe covered bridges are covered to protect the wooden flooring from snow.
Flooring is cheap.
Truth is, one of the jobs of a bridge tender in the old days was spreading snow on the floor of a covered bridge in winter so sleighs could get across. A few characters say the bridges were covered to prevent horses from getting spooked when they realized they were above flowing water, but about this theory we will not even speak. Made of heavy timber, these are the expensive part of the bridge, and if they fall apart due to exposure to the elements, so does the bridge. An unprotected wooden bridge will last maybe ten years. Put a cover over it, however, and it'll last for centuries.