It would be a toss up for me. If towing a trailer, personally, I'd stay on interstates during the winter. The two routes I'd probably choose would be either one of these depending on what the weather forecasts are in the areas I'd be going through.
Route 1:
South on I-5
to I-205 just north of Vancouver, WA
I-205 to I-84 just after crossing into Oregon
East on I-84 all the way through the Blue Mountains, through Idaho (Boise, Twin Falls), into Utah (through Ogden), just south of Ogden, I-84 will split from I-15, stay on I-84 to the point it intersects with I-80.
East on I-80 as it continues through Wyoming (Evanston, Laramie), and on to Cheyenne.
South on I-25 at Cheyenne. Continue on I-25 into Colorado through Denver and to Colorado Springs.
Route 2:
North on I-5.
Continue on I-5 to SR-18 just after going through Tacoma and Fife.
East on SR-18 through Auburn, Covington until the intersection with I-90 just west of North Bend.
East on I-90.
Continue on I-90 across Snoqualmie Pass, through central and eastern Washington, through Spokane and all the way through the Idaho panhandle, into Montana (Missoula, Butte, Billings), into Wyoming and through Sheridan. About 35-miles after Sheridan, I-25 splits off from I-90.
South on I-25. Continue on I-25 through Casper and Cheyenne, into Colorado through Fort Collins, Denver and to Colorado Springs.
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