Expanded from an earlier answer
From 1945-1955, Austria was under military occupation by the four Allied powers, much like Germany. Unlike its Germany, the geography of Austria and Vienna did not lend itself well to an easy partition. The military administration and occupation of Vienna was particularly cumbersome, with the Allies forming unified patrols (four men in a jeep) which was clumsy and did not lend itself well amidst the increasing suspicions of the early Cold War.
Much of this confused situation was the result of the Allies' muddled strategic planning with regards to Austria. Although the Moscow Declaration of 1943 had avowed that Austria was a separate nation that was the first victim of Hitler's aggression, the Allies behind the scenes held significant doubts about the viability of Austria as an independent state. Austria's seeming inability to resist Hitler in 1938 validated the opinion that the post-Versailles Treaty Austrian state was too small to keep out aggressors, but whose strategic location invited interlopers to interfere in Austrian politics. While Soviet foreign policy with regards to Austria was to keep their options open in the postwar order, the British floated various solutions such as a Danubian confederacy or a political union with Bavaria that would strengthen postwar Austria and prevent a resurgence of Prussian-German militarism. These plans proved stillborn for a number of reasons. Firstly, they often did not recognize the geographic complexity of the issue and many of the paper projects for an expanded Austria remained just paper. But the British-led initiative for an expanded or confederated Austria evoked uncomfortable parallels to the Cordon Sanitaire in the minds of the Soviets. Although Stalin had signaled to the British a slight commitment to an Austrian confederation in 1941, the Soviet position on a confederation had decidedly chilled by the Moscow Declaration. The Soviet press denounced a confederation as a resurrection of the Habsburgs and one that unjustly rewarded Austria at the expense of the other victims of Hitlerite aggression. But the problem of Austria still remained for Allied planners. The British Deputy Undersecretary of State Oliver Harvey encapsulated how the British saw this dilemma:
Were it not for the strategic importance of keeping Austria separate from Germany, we could let this flabby country stew. It is clear that Austria is doing next to nothing for herself and we shall have the greatest difficulty in infusing life into her after the war. There are no political leaders inside or outside the country who command any following. Austria will fall into the first arms which are opened to her.
Whenever the issue of Austria was brought up, Molotov would assert that an independent Austrian state was acceptable to Soviet interests, and even as late as 1944, Stalin showed some interests in an explicitly pro-Soviet Danubian confederation. in this context, the Americans' opinion on the matter became an important wild card. The Americans were reluctant to commit to a full-scale occupation of Austria and were content to push only for an occupation of Vienna. Both the Soviets and the British pushed for a full American commitment to Austria in order to relieve them of burdensome occupation costs. It was this pressure from their Allies coupled with the fear of a supposed "national redoubt " in the Alps that made the Americans switch course and commit to an occupation.
The first years of the occupation made Austria into one of the important sites for the early Cold War. The Americans' close proximity to Soviet troops and the unsettled nature of the occupation made it an epicenter for intelligence gathering operations. Although the Roosevelt State Department looked askance at the British plans for an Austrian-South German confederation. the Truman administration reversed course and proposed an East-West division of Austria in 1947, but the Soviets balked at this idea. The communist's electoral defeats in November 1945 Austrian elections had underscored to the Soviets the generally unfavorable attitude many Austrians held towards the Soviets. The fear in Moscow was that settling the Austrian question on terms proposed by the West would only benefit the West and undercut Soviet security. The result was stasis in Austria until the negotiations for the State Treaty began after Stalin's death.
After Stalin's death in 1953 and the resulting Thaw, the Soviets saw a renegotiation of the occupation as an opportunity to signal a new direction in the Soviet relationship in Europe. By negotiating an end to the Austrian occupation, the hope in Moscow was that the Soviets' position on a neutral Germany would gain traction in the FRG. On a more practical level, the ending of the occupation would end what was becoming a costly occupation for the Soviets. As negotiations for the Austrian State Treaty began, the Soviets staked out a basic position that Austria was to not seek a military alliance with an outside power and explicitly forbid any unification with Germany. A neutral Austria had an additional benefit to the Soviets by creating a gap in NATO's German and Italian front line, which would complicate NATO's existing military plans.
Many in the US State Department saw the Austrian State Treaty as Austria undertaking a voluntary decision to become another Switzerland. The Soviet's insistence on Austria's military neutrality was a marked change from other Soviet peace treaties. There was little concern of "Finlandization" in which the Finnish peace treaty with the Soviets also carried certain defense obligations that favored the Soviets. The Americans gambled that although neutral, Austria would politically and culturally align itself with the West. This gamble did pay off as the emerging political consensus in Austria was largely pro-Western.
The Western influence of the Cold War upon Austria was largely cultural. Austria's borders to the West were open, those to the Eastern bloc were, for the most part, not. American cultural missions flooded Austria with programs and materials as a part of the US's strategy of cultural diplomacy. Western products, tourists, and other connections further integrated Austria into the West, even if it could not join the various Western defensive alliance systems. Therefore, Austria emerged as something of an anomaly during the Cold War, culturally and economically connected to the West, but politically restrained by the Treaty from joining either Superpower bloc.
As the postwar order transitioned to normality, the emerging domestic political consensus hewed to the line that Austrians were at best only reluctant Nazis. Postwar cultural production, much of it dominated by Austrian conservatives (although there were a few Communist and leftist cultural movements), stressed Austria's quaint Heimat and history under the Habsburgs, such as the famous Sissi series of biopics about Empress Elizabeth of Austria. Within this postwar atmosphere, there was a great incentive for Austrians to keep silent about their activities during the war and the postwar economic reconstruction fostered a sense of Austria moving away from this dark interlude.
This larger amnesia received an internationally-sanctioned with the ratification of the Austrian State Treaty in 1955. One of the provisions for ending the Allied occupation was the formal disavowal of the Austrian state of pan-Germanism and any future unification with Germany. Austrian school curricula stressed Austrian distinctiveness and separation from Germany, as per the State Treaty, and minimized Austrian collaboration with the regime. Ironically, ending the Allied occupation became one of the founding national myth for the post-Treaty Austria as history textbooks and political discourse stressed the end of an undeserved occupation as a triumph for the new Austria.
Sources
Bischof, Günter, and Anton Pelinka. Austrian Historical Memory & National Identity. New Brunswick: Transaction Publishers, 1997.
Hills, Alice. Britain and the Occupation of Austria, 1943-45. New York: St. Martin's Press, in association with King's College, London, 2000.
Steininger, Rolf. Austria, Germany, and the Cold War: From the Anschluss to the State Treaty 1938-1955. New York: Berghahn Books, 2008.
Utgaard, Peter. Remembering and Forgetting Nazism: Education, National Identity, and the Victim Myth in Postwar Austria. New York: Berghahn Books, 2003.
Wagnleitner, Reinhold. Coca-Colonization and the Cold War The Cultural Mission of the United States in Austria After the Second World War. Chapel Hill: University of North Carolina Press, 1994.