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In the absence of more definitive information, I've assumed the titled city pair for your drive, in which case, the 'best' winter route would be I-74 to Champaign-Urbana IL, I-72 to Hannibal MO, US-36 across northern Missouri to St. Joseph, I-29 north to Nebraska City, NE-2 over to I-80 west to Salt Lake City and I-84/I-15 north and west to Pendleton OR and finish up on OR-11/WA-125 into Walla Walla. Of course, if your actual cities are different, some of that may not work. The main thing to keep in mind is that you want to use Interstates and major US highways wherever possible, you want to keep the route as short as possible, and you want to have some time (a day or so) extra in case you need to sit out some bad weather. You're looking at about 3½ days, again depending on exactly wher4e you're starting from and ending, so you'll want to have at least four days for the drive.

AZBuck