The sequence is the way the stops are visted. As long as you do not check on the "Reorder stops to find optimal Route", the sequnce is honored. If you find a case where this does not happen then please let me know.
Given that you are trying to solve a snow plough routing scenario, what are you inputing? Do you want the software to figure out the sequence or you are going to enter the stops in a certain way? At this point I would like to point to you that you should ask who ever as "assured" you that arc is up to the task, what task is arc going to do? I say this because the route solver with the "reorder stops to find optimal route" is called the Traveling Salesman Problem solver. The goal being to visit a set of stops in the best way. Snow plough routing is about visiting "edges" in the best way. And that is called the chinese postman problem or sometimes called arc routing or euler tour. ArcGIS is not designed to solve the euler tour. You can achieve good results by placing a stop on every edge and then setting a stop curb approach property to "No u-turn" and setting the solver u-turn at junctions property to deadends only.
Jay Sandhu