There have been a couple of threads asking what happened in the immediate postwar period:
http://www.reddit.com/r/AskHistorians/comments/1stom4/how_did_austria_manage_to_not_be_split_like/
The TL;DR is that Austria, like Germany, was split into US/UK/USSR/France occupation zones but for reasons expanded on in the links above, an arrangement was come to whereby all four powers withdrew in 1955 on the condition that Austria remained neutral.
In the immediate aftermath of the Second World War, Austria was divided into four occupation zones (like Germany) – a French zone in the west, a British zone in the south, an American zone in the north and a Soviet zone in the east. The capital Vienna was also split in four parts (but was surrounded by the Soviet occupation zone) and the very centre of Vienna, the first district (basically the old town) changed hands every month.
This occupation went on until 1955. The Soviet forces dismantled parts of the eastern Austrian industry and were generally not as well liked as the American soldiers, who were able to contribute to the rebuilding of Austria. There was an Austrian government and parliament, which was able to make laws, but these had to be accepted by the occupational forces before coming into effect.
There had been talks between the Austrian government and the occupational forces of independence, but the weren’t any real results until the early 1950s, when Eisenhower became US president and Josef Stalin died. In the end, Austria gained complete independence in 1955, but in turn had to adopt a constitution making Austria a neutral country (the Soviets had wanted this to gain a potential buffer zone beyond the iron curtain). It is said that the members of the Austrian delegation were drunk while making the final adjustments to the Declaration of Independence in Moscow, but still, on the 15th of May 1955 the declaration was signed by the foreign ministers of the occupational forces in Vienna and on the 25th of October, the last foreign soldier left Austrian territory. The 26th of October – the first day of free, independent and neutral Austria – became our national holiday.
All of this is important as Austria’s neutrality was an important factor during the Cold War. Unlike nowadays (where Austria is associated – though not a member – with NATO and has agreed to participate in future EU battlegroups, etc), Austria was actually neutral during the Cold War, although public opinion can be described as US-favourable. Due to Austria’s geopolitically important location, Vienna became the seat of many important international organisations, such as the UN, OSCE, IAEA, OPEC, etc). Austria also tried to act as a mediator between the two blocks in the Cold War, with the most notable event being the meeting between JFK and Khrushchev in Vienna in 1961).
When social democrat Bruno Kreisky came into office in 1970, he not only mediated between the USA and the Soviet Union, but also tried to solve the conflict in the Middle East and became one of the first western politicians to hold talks with the likes of Gaddafi or Arafat. Generally speaking, Austria’s focus on foreign policy was never as big as during those years.
Other important events concerning Austria in the Cold War were the Hungarian Revolution in 1956 and the Prague Spring in 1968, during both of which thousands of refugees fled across the borders into eastern Austria. Many went on the other countries, but some remained in Austria.
The importance of Austria dwindled after the end of the Cold War, so we joined the European Union in 1995. This would not have been possible during the Cold War as there were grave concerns that an EU membership would violate the (constitutional) law on neutrality.
tl;dr: Austria was divided like Germany, full independence in 1955, neutrality, important mediator in world politics, loads of refugees came in from the east.
Sources and further reading: