If not the fairgrounds, other local land owners and live stock holders can agree on a safe pasturage site. This works in flood zones in King and Lewis counties.
Local responders and EM generally don't have the resources to take water trucks to fill n inflatable pools every day; better to move your animals to the water until the floodwaters subside and local water sources are restored.
Oops, I had a morning brain cramp when I wrote this - opening the fairgrounds would definitely not work in Lewis County, as Susan points out the fairgrounds are thoroughly under water in most any flood. What I meant to say at 8.30AM without benefit of coffee was that the pre-planning among local land owners and live stock holders on safe pasturage sites works in Lewis and King County. But only the King County fairgrounds in Enumclaw is above the high water mark - it may be in the flow of a lahar off of Mt Rainier, but if the lahar is your disaster I submit horses and owners have far more important problems than potable water.
Also it may be that Island County EM does have a plan to cart water to horses and not to cart horses to water, but Island County is made up of smallish islands with some unique capabilities and needs: they may have a water carrying vehicle stationed on islands with significant animal populations and a plan to water them. That's fine on smallish islands, but it generally doesn't scale if you were talking county-wide animal watering in most counties (including King).