Actually what the law states is (extracted from Library of Congress Congressional Record):
"(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."
Notice the absence of any specific license requirement.

It specifically depends on the laws of the State that the National Park or National Wildlife Refuge is located. Anti-gun people have brought up this issue.
Note: The law that restricts firearms in Federal Facilities is still in effect.
Respectfully;
Jim