As others have said, it's not a difficult drive. Going UP from Buffalo, it's a very scenic drive, not overly steep, but a bit curvy. You'll pass a lot of dude/guest ranches in that area.
Going DOWN, it's a somewhat long decline to Ten Sleep, but again not overly difficult. Follow the advice of the folks above.
One thing to be aware of...this highway is very popular with motorcyclists, so you want to be extra cautious on curves, just a heads up that they might be coming the other way, or from behind, may pass you when the opportunity arises.