Yes you can legally carry guns in State parks as long as the gun is legal and you have the permits for the gun you have.
Starting Feb. 22, 2010 Congress passed a law stating that people are legally allowed to open carry or conceal carry guns on them even when loaded in State Parks.
As long as you're legally allowed to carry the gun or guns and have a permit to carry those guns then you can legally carry guns loaded or not into state parks.
I would see no reason to carry a gun into a state park unless you want it for protection but being in state parks are pretty safe.