The shortest/fastest route on Google Maps is US395 SW to I84, I84 SE to Twin Falls ID, US93 straight south. On this route there may be snow across Washington (there is now), a grade over Cabbage Patch Hill, and high desert across Nevada.
A close second is I90 east to I15. This is an all freeway route. The highest passes are on the ID/MT border, around Butte, and on the MT/ID border.
I84 west to Portland, and I5 south avoids that inland cold, but at the cost of several extra hours of driving. Plus heavier traffic in California.
US97 and US95 are other options.
