The commission may adopt and promulgate rules and regulations permitting pets, domestic animals, and poultry to be brought upon or possessed, grazed, maintained, or run at large on any area or portion of any area under its ownership or control. Any person who brings, possesses, grazes, maintains, or permits to run at large his or her pets, domestic animals, or poultry on any area or portion of any area under the ownership or control of the commission, unless the commission has permitted such bringing, possession, grazing, maintaining, or running at large, shall be guilty of a Class V misdemeanor.