RCW 9.41.060 Exceptions to restrictions on carrying firearms
The provisions of RCW 9.41.050 do not apply to:
(8.) Any person engaging in a lawful outdoor recreational activity such as hunting, fishing, camping, hiking, or horseback riding, only if, considering all of the attendant circumstances, including but not limited to whether the person has a valid hunting or fishing license, it is reasonable to conclude that the person is participating in lawful outdoor activities or is traveling to or from a legitimate outdoor recreation area
I don't know if going to the park qualifies, but it is an outdoor activity in my book. I doubt if many Law Enforcement or Wildlife Officers are even aware of this law. Go butterfly watching, carry loaded and concealed from time you leave house, in your vehicle and until you return home. Jogging would qualify.