US93 is (mostly) 2 lane, but I wouldn't describe it as 'secondary'. Here in Washington they are just a diligent about plowing US2 as I90.
The only pass on US93 is Lost Trail on the state line. You'll be over it the first day, so if you leave when the conditions are good, you'll be fine. If conditions are bad on Lost Trail, they are likely to be bad on other routes out of Missoula. I90 to the west crosses 2 passes on the way to Washington. To the east it meets I15 at a high point. I15 has a pass on the state line - though it isn't quite as high as 93, and broader.
Once in Twin Falls you still have the choice between staying on 93 or taking I84 to I15 in Utah. I15 v US93 has been discussed many times. People like 93, but acknowledge that it is more remote. I15 has SLC traffic.