There are many elements that are presented in the novel Animal Farm that can be found in real historical events. This is because the book is meant to be an allegory of modern political systems.
For example, the Russian Revolution can be compared to the rebellion in the farm. In the Russian Revolution, the workers tried to take control of production away from the elites who had owned it so far. This is similar to how the animals took the farm from the farmer. The Russian Revolution also culminated in a society controlled by a single party and which operated in a cooperative way, with strong central control. This is the same way in which the farm operates once the animals take over.
In terms of WWII, a parallel that we can find is that of the rise of strong leaders and the cult of personality. During the war, characters such as Churchill, Hitler, Emperor Hirohito and Mussolini were presented as being extremely powerful, capable and larger-than-life, with support among their people being extremely high. This is the role that the pigs try to adopt in the farm.
Finally, a parallel that we can find when it comes to the Cold War is the use of propaganda. During the Cold War, the United States used propaganda and repression in order to convince the population of the dangers of communism. In the same way, the Soviet Union used these methods to discourage the ideas of capitalism. The use of propaganda to scare and manipulate people is shown in the book, when Napoleon attempts to create crazy and unfair stories about Snowball.