Independent of political reasons, travel for private persons was greatly restricted until 1949.
Churchill feared, correctly, that politicaly a division was being created by the Soviet Union to separate their area of influence from that of the Western Powers.
Occupied Germany was still (in 1946) under common Allied control, so Germany was excluded by the use of the city name Stettin
- which was situated right/east of the red area near the Baltic sea
In reality the city name of Lübeck could have been used
- which was situated left/west of the red area where the thick black line starts on the Baltic sea
- the purple was part of the agreed Soviet Zone
- whick they occupied in July 1945 after the US troops withdraw
- Berlin was not part of the Soviet Zone
- but was subdivided into Sectors under common Allied control
- the common administration of the city effectively ended during the Berlin Blockade in September 1948
After occupying their Zone in Germany, the Soviet Union started immediately to fortify their border to the US and UK Zones with bob wire.
Following the military occupation of Germany in May 1945, civilians were initially only allowed to leave their place of residence or its immediate vicinity with a permit from the garrison authority of their zone. By June 1945, the bus and train service within the respective garrison zones had been resumed on many stretches. However, the public train service did not run between the garrison zones. Nevertheless, there were numerous travelers who crossed the extensive uncontrolled boundaries between the garrison zones on foot, by bicycle or by hitch-hiking.
On June 30, 1946, the boundary between the Soviet garrison zone and the Western garrison zones (the American, British and French zones) was blocked. The Soviet military administration in Germany (SMAD) had previously asked the Allies to secure the line of demarcation to the Western zones. A special identification card, the Inter-zones Travel Passport (Germany), known as the inter-zones passport, was introduced by the Allies. This had to be applied for by citizens wishing to travel in occupied Germany.
Not sure if the same is true for the areas inside Austria. The systematic closing of the borders started on the 26 May 1952, which included the borders between the Western Sectors of Berlin and the Soviet Zone.
It is assumed this is what led to the 'Iron' in the term used by Churchill.
For Czech border it was not so much the case in 1946, since the Soviets had less control there until the 1948 Czechoslovak coup d'état.
In general, travel for everyone (East and West citizens) was greatly restricted. Permits were needed for everything.
Another problem was documentation of the individuals were in a sorry state.
I have seen Polish passports, issued for persons to work for the polish government as a representative to the US Military government in Frankfurt. Almost 1/3 of it was filled with the needed permits to travel and stay there (add to that return trips home for consultations).
For an individual, even with reliable documents, it would have been very difficult due to the general chaos that exsited on both sides.
Add to that any political reasons against emigration that any of the local governments may have had, then 1946-49 were not good years for travelling.