Honestly, I don't see what the first two paragraphs you posted has to do with your argument. To me, it reads that it was ok for the Police to search you when you're under arrest, and this means to me they'd need a warrant to search whether you're walking down the street, driving, or are being arrested in your home (with a warrant for the arrest of course).
I get what you were saying, my point was that while Colorado may have statutes allowing you to get away with having a loaded pistol in a car being open carried without a permit (due to extension of the home), Washington state does not have such provisions and as such, it is 100% illegal for someone who does not carry a CPL to carry a loaded pistol in their vehicle, open carried or otherwise.
See: RCW 9.41.050
"(2)(a) A person shall not carry or place a loaded pistol in any vehicle unless the person has a license to carry a concealed pistol..."
This leads me to believe that extension of your dwelling with regards to firearm carry does not apply nationwide.
Edited for typos