Battle of Cowshed is a stand-in for the Russian Civil War.
The Civil War wasn't fought between the people and the tsar—because the tsar was already dead. It was fought between the Bolshevik Red Army and a motley crew of landowners, middle-class citizens, monarchists, and old army generals. (You know. The squares.) These people had two things in common: they hated the Bolsheviks, and they called themselves the White Army.
Key fact: in 1917, the world was smack in the middle of a little conflict called World War I (or the Great War, in 1917). By 1918, German attacks were a little too close to home, so the Bolsheviks signed a treaty to end the war. Trotsky (a.k.a. Snowball) didn't want to—but the Bolsheviks didn't have a choice. Their country was in uproar, and the White Army seized on the treaty as a sign of weakness.
The White Army wasn't alone. It had help from foreign countries like the U.S. and U.K., who were super concerned about something they called the Domino Effect: the idea that communism would spread from Russia, knocking over capitalism countries like so many dominoes. These Western countries sent in reinforcements, just like Mr. Pilkington and Mr. Frederick help Mr. Jones try to win back Animal Farm.
They failed. By the end of the Battle of the Cowshed, the animals have won, the Bolsheviks (um, pigs) have taken over, and Animal Farm is established. Sorry, Mr. Jones. Off to Ekaterinburg for you.