Wy state park rules are found at the link below. Nowhere does it say that you can't have a firearm in a state park.
Section 16. Public Safety.
(a) Unless otherwise provided on park lands, no person shall:
(i) Possess explosives of any kind on park lands.
(ii) Use or display any weapon in a threatening manner.
(iii) Discharge a firearm or other projectile device, or otherwise purposefully or negligently endanger the life of any person or creature within any park lands. The discharge of a firearm or other projectile device while engaged in hunting or fishing as authorized by Wyoming Game and Fish Commission regulations is authorized except within 400 yards of any public use facility or activity area, including picnic areas, campgrounds, private cabin and concession areas, boat ramps, hard surfaced roads, designated trails, and parking lots.