The route between the two cities has always been known to wind its .......... way through steep mountain passes and coarse terrain.

From the sentence, we see that the adjective should present the "way" that is able to navigate through steep mountain passes and coarse terrain. 
We can eliminate easy and smooth since they present the way to be easy to traverse, while the sentence suggests otherwise 

Elusive would mean something that is difficult to catch or find which does not fit the given context. 

Tortuous means something that has a lot of twists and turns and is complex. This would best fit as an adjective to the path wind will have to take to cover the difficult terrains. 

Therefore, Option D is the correct answer.