i don't know about Oregon but California has 3 categories of chain control.
R1 is the usual stuff: non 4WD vehicles have to chain up their drive wheels and 4WD vehicles that have M+S tires w/ at least 6/32" of tread are not required to install chains, but are required to carry them in the vehicle. R2 is more restrictive and if it gets to R3, they just close the road. so, R1 is generally all that you'll run into.
during that super snowy week in January, up at Tahoe, i got away w/ 3/32" of tread. i had to dig the vehicle out of the previous night's snowfall, twice, but i never had to put chains on. i did carry chains in the vehicle and i did drive cautiously.
when i wrote chains above, i meant cables. my vehicle is lowered so i didn't even try to fit chains on it.