Hello,
I had made that trip about 6 years ago in the autumn. It can be a very beautiful drive.
Seattle winter weather normally is not cold enough for snow. You will more likely encounter rain. And as long as you keep a reasonable distance from the car in front of you, you should be fine.
Though it does not snow in the NW often, we do see snow occaisionally. But on the major highways, this should not be a problem. Because of the high traffic, those roads are the first to see the plows and salt trucks. Again, just be sure to maintain a safe distance.
When I drove to Vegas, I cut through Washington in I-90 east to I-82 and I-84 down to Twin Falls Idaho. From there I took State Rout 93 all the way down to Vegas. SR-93 is much more minor road. It's single lane in both directions and takes you through some desolate ranch lands.
This is the most direct route. Though there really isn't a whole lot to see along this route. The one thing that I would say is a must is stopping for some wine tastings in Washington. I-82 runs through the heart of WA wine country. There are several tasting rooms just off of the highway that offer free tastings. Some wineries do charge a small fee.
Here's a US Road Map for an overview of our highway system. http://www.fhwa.dot.gov/planning/images/nhs.pdf
This site has a detailed road map of each state. http://www.milebymile.com/main/United_States/Washington/maps.html
And sites about WA Wine http://www.winecountrywashington.org/ http://www.washingtonwine.org/
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