Living just a few miles from the OP...
Washington State has no restriction on the movement of firewood with-in the state. It does not have any rules on moving firewood from Oregon either. I don't believe that it does from Idaho either. They prefer that you move wood with no bark.
However, that's the end of the list. You can't bring in wood from any other state, nor Canada.
Some National Forest districts do have restrictions but they change often enough I don't try to track them.
Montana and Oregon do NOT restriction firewood from Washington. But Canada and California do.
Oddly Washington has an additional "gotcha". If you are moving Maple, Alder, Cedar or Yew, and lack the proper paper-work (bill of sale, bill of lading, etc) you can be ticketed, arrested, have the wood confiscated, etc. This is NOT over firewood, but rather those are the most common woods to be stolen by "timber rustlers". As an example a 1-inch thick blank of AAAA quality Maple, large enough for an electric guitar can retail for $400.
Personally I carry wood "in-side" more due to the wet/rain/fog/damp/dew we have then anything else.