I can't find any specific corroboration of this, but it was fairly common for movie stars (which Cooper certainly was at the time) to receive deferments. It was the general feeling of the government that movie stars could better serve their country as, well, movie stars (by appearing in patriotic movies) than by slogging across Europe as an unremarkable soldier.
Cooper in particular appeared in 1941's "Sergeant York", a movie about highly decorated WWI hero Alvin York.
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Drafted.
DS
Women were, and are never DRAFTED. only men.
During World War II, men of military age were drafted into the war.
In World War II 300 million British men were drafted. 800,000 children were drafted, and 80 million pregnant women were drafted, but only 79 million pregnant women actually fought in the war.