You pose two questions, each of which has (possibly) a different answer.
Typically, the courts will look to the "intent" of the occupier to ascertain whether the situs is an abode.
Generally, for purposes of "search and seizure," the courts will look to how readily apparent the contents of the situs are exposed to or hidden from plain view. The more hidden, the more the courts are going to view the situs as being an area where the resident has an expectation of privacy, regardless of how long the occupier intends to occupy the situs.
For purposes of RCW 9.41.270, the courts are likely to look at how "permanent" the situs appears to be in determining whether it qualifies as an "abode." A weekend tent erection is probably much less likely to be deemed an abode, whereas a summer-long tent erection will better lend itself to be deemed an abode. This may, however, be a more fluid determination if the occupier of the tent has no other residence, even if the tent is moved on a periodic basis (e.g., tent "cities" that have moved around the Seattle area over the past few years). Such determination is most likely to be made on a case-by-case basis and is likely very fact-specific.
Again, in most cases, a court will probably endeavor to determine the intent of the occupier.