Smokey Mtns don't exist. Smoky Mtns do. :)
In any case, Utah and the path to there is a very desolate place for much of the path, and you have to go over major mountains to get there from MN. If your truck has any issues with overheating, it will be tested either going to Zion or the Smoky Mtns.
A primary consideration should be the weather. The Smoky's are great in Spring. You can expect significant snow on the way to Utah until June if not later.
Don't underestimate the importance of knowing how far you can go between tank fulls if you go West. If you haven't been out West much, keep in mind that it is normal to be 100 miles between open gas stations and cities of significance or more. Plan your stops. Be self-sufficient.
I suggest a shorter trip first. In that end, the Smoky's might be easier. You don't exactly completely leave civilization to get there. If you find you don't have what you need, you can easily pick it up.