I am curious if there is a route where snow isn't a huge problem and that won't take an eternity. Here are the options I considered.
Drive through Boise, ID, through eastern oregon and eastern washington and over the cascades. Problem: Blue Mountains in Oregon and Cascades could have really inclimate weather.
Drive up to Missoula, MT and then drive I-90 to seattle. This will effectively take the Blue Mountains out of the picture but you still have the Cascades and who knows what kind of snow will be in Montana.
You can't avoid the Blue Mountains unless you go way to the south and go through like Carson City or Reno, NV. The route through Carson City or Reno will take you up into Medford and then you can go up I-5. Problem: That route will scrape the eastern part of the Sierra Nevadas.
You don't have to go through Nevada, you can just go straight through southern oregon to Medford and then up I-5. But that passes close to Crater Lake where I heard snow can be quite the problem as well. Is there really no solution? I could go to sacramento and then up I-5 but that would take an eternity.