Ideology was certainly important to the origins of the Cold War. To put its significance in perspective, it is important to remember that the United States had been among the nations that sent troops to Russia in support of the anti-revolutionary "Whites" during the Russian Civil War. Furthermore, the 1920s saw a swell in anti-communist fervor in the United States. So the Soviet Union, had been, from its very beginnings, the ideological rival of the United States.
Basically, the ideological differences between the two powers helped create the mutual atmosphere of distrust that characterized the early Cold War. This was because they caused each to interpret the actions of the other in the worst possible light. Stalin's actions in Eastern Europe in the wake of World War II, for example, were interpreted by the United States as the beginnings of a plot to expand communism around the world and to destroy the way of life of the United States, one that as analyst George Kennan famously observed, had to be relentlessly resisted:
In summary, we have here a political force committed fanatically to the belief that with US it is desirable and necessary that the internal harmony of our society be disrupted, our traditional way of life be destroyed, the international authority of our state be broken, if Soviet power is to be secure.
On the other hand, Soviet communist ideology, focused as it was on a constant struggle between communism and western capitalist society, tended to interpret the actions of the United States as inherently aggressive. The Marshall Plan, for instance, was seen as an imperialist attempt to expand American power into Europe, rather than as an attempt to assist in rebuilding the shattered European states. So ideology played a crucial role in escalating conflict in the wake of World War II.