Butterfly effect is first coined by meteorologist Edward Lorenz in 1981 which basically says a seemingly insignificant event such as a flap of a butterfly's wings can influence the details of a hurricane's path. in this case, the flapping of the butterfly's wings would be Napoleon's cold and the hurricane would be Napoleon losing the war.
I don't have problem with Tolstoy scorning Napoleon's cold for bringing his demise just like a butterfly's flapping can alter the hurricane's path because I myself don't really believe in the claim either. But I do think Tolstoy is too assertive when he says the soldiers are fighting on their own accord and rulers are nothing but pawns to fate. Even if the soldiers are fighting out of free will, they are fighting for something which corresponds to Napoleon's and Alexander's wish. And who has instilled in these soldiers to act toward that certain goal? Tolstoy calls them figureheads, but they hold some power that allows them to lead history in one direction rather than another. Of course, Napoleon's decision arises from the need to secure his rule over the territories he conquered; so he decides to invade Russia. In this way Tolstoy correctly says people, not only the rulers, contribute to history as mediums of fate even when they make decisions based on their free will-- because the decisions made with free will are reactions to the situation.
However, Tolstoy neglects that such reactionary decisions are at the same time catalysis of new events, and people are actually building history instead of fulfilling fate by making their own contributions. Since not all people can contribute to history in a significant way, there needs be a central force that directs history. The rulers are tasked with giving directions by the merit of their position (no matter how ineligibly or unfairly they acquired it). In this way Tolstoy's claim that the rulers don't do anything is untrue, because they have more power to direct people to set off a new course of history.