Eugene OR to Shawnee OK in Nov

FYI max combined tow length in Oregon is 65'.

Depends on the weather. Keep an eye on it. Interstates are your best bet. If it snows head south. Don't agonize so much about it. Just be flexible with your plans. Sometimes you just have to wait a day, maybe 2 at the most for a Nov snow storm to melt.

The route time isn't that much longer to go south.

South of Eugene before Ashland there is a series of 1000-1500' passes that can also get snow, but they usually remain open.

Just south of Ashland is the Siskiyou Summit (4300') which can be an issue and it's unpredictable. I've been stuck, heading north, when it was closed. Sometimes it reopens quickly other times it can take a while.

Between Ashland and Redding you're in potential snow country will need required to carry chains. If you don't have them, get them. If you can find a national chain that allows returns you can do that, if not hang on to them.

I'd already posted the link to Oregon's TripCheck so here is Caltrans

What has been stated....you will need to carry chains for the MH and also the car trailer.....and the max length in Ca. is 65' also.