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This question comes up time and again, and there are really only two simple rules to finding the safest driving strategy in the winter. (1) Find the most direct, all-highway route. (2) Leave time in your plans to simply sit out any bad weather. Adding hundreds of miles to a journey in a futile attempt to find a 'snow free' route is just plain counter-productive. There is no such route anywhere in the continental United States, and adding miles simply increases the time you'll be on the road and subject to untoward weather.
In your case the best route depends very critically on where those 'few stops in Oregon' are. Without knowing where the serious cross-country portion of your trip is going to begin, we really can't tell you how you should go. But in general, the drive from Seattle would take a minimum of four solid driving days and you should budget a fifth day for the trip to handle any inclement weather you come might come across. Please dissuade yourselves from any idea that one of you can drive during the day while the other drives at night. You will need both of you awake and alert to keep this trip safe.
AZBuck