National Parks: no carry at all. Firearms must be unloaded and locked away in your vehicle.
National Forests: defensive firearm carry regulations subject to state law; in Virginia the general assembly has assigned this function to the Department of Game and Inland Fisheries (DGIF), which, to its continuing shame, allows only concealed carry with a valid permit. Some people don't know that OC is not permitted in NF, and they have reported that the DGIF officers don't seem to care, but don't chance it. Obey the rule for now, we're working on getting it changed some day.
Public roads: OC is fine. If you are on a private campground, you are fine until the staff tells you otherwise, at which time you should decide to take your business somewhere else.
Virginia is generally very carry-friendly, but DGIF has a bug up it's ass about pistols for some reason.