If you get pulled over in states that require brand inspections, which most western states do, and you do not have one, they can confiscate your horse until a brand inspector shows up and finds out information on your horse, etc. It doesn't matter if you have paperwork that shows the horse is yours, registrations papers, bill of sale, if a brand inspection is required, you can get a HUGE fine and the horse can be stabled until a brand inspector deals with it.
In Wyoming, even if you cross county lines, if you don't have a brand inspection, you can be turned around and not allowed in the county.So, crossing state lines without one is even worse. Same as a Coggins, if it is required, and most states require a current one, if you are asked to show your Coggins and do not have one, the horse can be stabled and has to stay there until a Coggins is drawn, sent in and received back.
Here is the law pertaining to Washington. They require brand inspections going into or out of Washington. Plus,Transportation of livestock on the public highways of the state must be accompanied by an official certificate of brand inspection or an original certificate of permit.
Brand inspections don't cost much and so much easier to carry the paperwork in the trailer for wherever you go.