Unfortunately they don't, in fact they don't allow firearms at all in most cases. If they do it will be in conformity with local law, which will allow concealed carry for those properly licensed in the particular jurisdiction. Which is most cases is a very small population, in state permit holders or permit holders in a reciprocal state.
IMO carry should be allowed on federal land for anyone who can legally own a firearm, period. If not concealed, open.
Otherwise, your correct, you would need a permit to carry the loaded gun while hiking on the trail. That could be a concealed carry permit, or a hunting license. You might have to convince the ranger your 9mm is an appropriate hunting gun.