Did the existence of nuclear weapons cause a dramatic change in the conduct of foreign policy or the options available to nuclear states? Why or why not?
To answer this I'll off with a quote from Mao Tse-Tung: Weapons are an important factor in war, but not the decisive one; it is man and not materials that counts. To get to the crux of issue whether nuclear weapons caused a dramatic change an examination of linking the military and weapons to the policy creating branch of the government.
We can think of the state, the military, and the people as closely linked. The people creating the state and the state utilizing the people as man power and tax base to create a military. The relationship between the state and the military has four levels of command. There is the tactical,operation/theater, strategic and then the political/policy. The policy is created and consequently commands and actions flow from it. Policy is linked to strategy linked to operations linked to tactical. Adding another layer to the analysis are the concepts of confrontation and conflict. Confrontation is where there is a clash of policy but doesn't mean a war or a conflict. A conflict is what we think of as war.
During the Cold War the over arching policy towards the Soviet Union was containment. As argued by George Kennan in the article “The Sources of Soviet Conduct,” the idea of containment was to rely on the Soviet Union's history to focus on socialism and power consolidation at home as opposed to an ideological supporting of all communist movements abroad. The view was, far as the Kremlin was concerned, “ “It has no right to risk the existing achievements of the revolution for the sake of vain baubles of the future. The very teachings of Lenin himself require great caution and flexibility in the pursuit of Communist purposes.”
Kennan goes further to say about the internal situation of the Soviet Union: “The mass of the people are disillusioned, skeptical and no longer as accessible as they once were to the magical attraction which Soviet power still radiates to its followers abroad...In these circumstances, there are limits to the physical and nervous strength of people themselves. These limits are absolute ones, and are binding even for the cruelest dictatorship, because beyond them people cannot be driven...The present generation of Russians have never known spontaneity of collective action. If, consequently, anything were ever to occur to disrupt the unity and efficacy of the Party as a political instrument, Soviet Russia might be changed overnight from one of the strongest to one of the weakest and most pitiable of national societies.”
The Russians were more concerned with their own ideological and physical preservation on the international and domestic level. Second, on the international level they were not going to put their neck out, so to speak, for any other socialist or communist movement that didn't serve the self-interest of Russia. Last, the domestic level was corrupt and wasting on the social and economic level. Thus the policy of containment acted as an expansive box, letting the Russians expand within limits until its core collapsed and along with it the Soviet Union.
The policy of containment was laid out but the problem became how to actually box the Soviets in? The answer was provided via nuclear weapons. Nuclear armament was first, if only, weapon to be able to attack the people, state, and military simultaneously, effectively, and with massive destruction. Whether the weapon was tactical or strategic in nature, the design was to make the mark permanent and force or destroy the hand of state receiving the blow. This is the basis of nuclear strategy, destroy the military on the field and force a political solution or destroy the people/state and be the default victor. Whether it was “massive retaliation,” “flexible response,” or “arms reduction,” the crux of the nuclear threat stayed the same: massive loss and costs being inflicted on both sides.
Back to the original question of whether: Did the existence of nuclear weapons cause a dramatic change in the conduct of foreign policy or the options available to nuclear states? No. At the core of conduct of foreign policy is national interest as defined by context. In this case, the context was the Cold War and the confrontation with the Soviets that was driven by Kennan's idea/policy of containment. Successful policy isn't driven by the weapons used on the strategic, operational, or tactical levels but rather people who understand the national interest of the state. Both the Soviets and United States understood that the cost of nuclear use was high so both had their own form of deterrence and containment. The Soviet hope was that capitalism would collapse and the workers unite. The Americans read the problem as one of history and culture that could be countered given the right policy. Ultimately containment proved be the more successful policy. (Notice also that the Soviets viewed the problem ideologically while Kennan's analysis was rooted in history and culture.) It was one set of defined national interests versus the other.
Given the long view of history was the introduction nuclear weapons dramatic? Again no. If nuclear weapons are dramatic or game changing why didn't the game change? The use of nuclear weapons, unlike air planes, tanks, or the automatic rifle, was so destructive that no state wanted to shoulder the cost. In other words, states are focused on survival and the pursuit of self-interest, all nuclear weapons did was reify the former and made the latter conservative and limited as to avoid nuclear holocaust. It made international affairs not the realm of constant change and flux but rather the art of status quo preservation.
The one issue I wold raise vis a vis nuclear weapons being dramatic is proliferation. Once the Cold War ended all the technology, weaponry, material and most importantly knowledge of the Soviet Union nuclear program scattered to the four corners of the earth. Thus nuclear weapons is no longer restricted to the purview of a controlled few but slowly and surely to the rest. Thus the dramatic shift nuclear weapons cause in terms of conduct is not the actual possession of weapons but the knowledge to produce said weapons. Truly the genie has been let out of the bottle.