After digging around on the WV state parks web site, this is the only thing I could find:
Uncased firearms, uncased bows and uncased arrows are prohibited in state parks, state forests, and state wildlife management areas, and on state trails, except:
When the area is open for hunting (hunting is prohibited in state parks) or when a registered park or forest guest has the written permission of the area superintendent to carry them in a case from his or her lodge room, cabin or campsite to open hunting areas, or to an officially designated rifle, pistol, skeet, trap, target or shooting range;
Area superintendents may authorize their use in historical reenactments and plays; and
The Chief of Parks and Recreation, Division of Natural Resources, may authorize their use for a limited period in conjunction with recreational and arts and crafts programs.
Doesn't say anything about loaded or unloaded. I wonder if a fanny pack would qualify as a "case" making it possible to carry a handgun. Having to case a long gun would seem to make carrying one a practical impossibility. I think your only option may be to call and get an official opinion.