The law allowing firearms in National Parks was passed as an amendment to H.R. 627 the Credit Card Act of 2009, and may be found in Section 512 of the law. The relevant section of the law is this:
(b) Protecting the Right of Individuals To Bear arms in Units of the National Park System and the National Wildlife Refuge System- The Secretary of the Interior shall not promulgate or enforce any regulation that prohibits an individual from possessing a firearm including an assembled or functional firearm in any unit of the National Park System or the National Wildlife Refuge System if--
(1) the individual is not otherwise prohibited by law from possessing the firearm; and
(2) the possession of the firearm is in compliance with the law of the State in which the unit of the National Park System or the National Wildlife Refuge System is located.
How does this affect California visitors to National Parks? While I am not a lawyer, every gun owner should be knowledgeable about the gun laws in the state, which are complex. A very good resource for this is "How to Own a Gun & Stay Out of Jail" by John Machtinger, who is a lawyer. Every gun owner in California should own a copy of this book and read it thoroughly.
My reading of the laws gives me this interpretation:
Gun owners may now possess their firearms in National Parks. If you are traveling in your vehicle all firearms must be unloaded, and handguns must be stored in a locked container. You may have loaded firearms in your campsite, however, if you are a backpacker, carrying your handgun, whether loaded or unloaded, is a violation of the concealed weapon law, unless you have a California CCW license. Open carry of a handgun may or may not be legal depending, I think, on the county. Open carry of a rifle or shotgun may indeed be legal, but since hunting in a National Park is not allowed, perhaps not. I do not know of a good resource for open carry in California, and would welcome a resource.
I think that more interpretation of California law will have to be made, and rules published to make this issue clear. At the current time the only things I will attempt with my firearms are traveling through a National Park (Highway 120 anyone?) and camping in a site reachable by motor vehicle.
In any case, do not try this until the law comes into effect, which in Section 3 is "9 months after the date of enactment of this Act, except as otherwise specifically provided in this Act".