So my neighbor has 1 acre of property. It is divided into 2 sections. Both sections are completely muddy. There are a total 4-8 horses she keeps in there. She sometimes will move 2 horses to her back yard which is 1/8 of an acre.
If the property in question is located in or near the shoreline of Puget Sound or a watershed that drains into the Sound the rules get really tight. They don't want runoff from animal waste getting into Puget Sound. I know you can't even build on waterfront property in some areas without meeting all kinds of restrictions on septic and drainfield requirements.
A couple places to check that might have more information are the Pierce County Extension office and Horses for Clean Water: Contact | Horses For Clean Water