If you scroll down to the bottom of that link you'll see the ORS (without it stating that it's the ORS) and the 6,500 lbs requirement.
ODOT only cares about it's administrative rules, which are enforceable to motor carriers, but are not actual laws in the state of Oregon. So they put up these signs and most people take them as the law. If you're not in commercial service, the citation would be for ORS 815.140. Though I'm not sure that many troopers or deputies are that well versed.
I doubt 815.140 citations are ever issued for 2500s or 3500s unless running summer tires or 2wd. My guess is those violations are used for the semi driver who fails to chain up and gets stuck.
And back to the original point, I wouldn't hesitate to roll a 3500 with traction tires (and 4wd) any more than I worry about running my PW over its GVWR (but under other 2500s GVWR). I cross the cascades 50-60 times per year and cannot remember seeing 3/4T or 1T trucks with chains. The only chains I see are on FWD passenger cars and commercial vehicles (>26,000 lbs).
And, while not on topic, airing down should be the number one tool, not chains. Even at 9,000 lbs I run 35psi for good traction white roads and 20-25 for more naughty stuff. Airing back up, of course, when conditions change. 35 may seem low, but if you look at a tire inflation chart E rated tires are usually good for 2,300 lbs at that pressure. Obviously need to know your axle weights and do the math for what is right for your load and conditions.