I see you are in WA. You must carry tire chains with your 4x4. You do not have to put them on unless signs say "All vehicles must use chains". You state that you are over 10,000 pounds. This puts a slightly different light on subject.
Most other times you can travel in four wheel drive.
From WSDOT website.
WSDOT winter driving4WD/AWD and chains
4WD/AWD vehicles (under 10,000 pounds) do not need chains installed during "chains required" notices, but drivers still must carry chains with them in case conditions worsen and they're required to install chains during a "chains required on all vehicles" notice.