What I would like to see is diplomacy that means something, and organisations that mean something. The organisations that I see as most vital to this time period are the United Nations, the United Nations Security Council, the WARZAW pact, NATO, and the Non Aligned Movement.
I would like to see the player be able to interact with these organisations in some meaningful way. Perhaps via some intelligence actions you could see that the Soviet Union is deploying nuclear missiles to Cuba, then you could have the option to bring it up in the UN, the UNSC, NATO, etc, and to influence other nations as a result.
I know the USSR and the US each had veto holding seats since the creation of the UNSC, but I would like to see some sort of UN and UNSC function in the game.
I would also like to see some economic and political options for the games you play where you are not the Soviet Union or United States to make the game somewhat fun for non US and non USSR players.
I would also think there should be a good arms selling functionality, because it is in the Cold War that the USSR and US/France/UK sold weapons t others nations as a way to gain influence, and even to fight proxy wars as was the case for the Arab/Israeli wars for example.
In a Cold War game, you also cannot neglect black ops, or intelligence, or secret service type abilities for the player. A large part of the Cold War was the US building strategic partnerships and doing coups to get rights for listening posts all along the Soviet Union to help spy on the Soviets, there was a huge effort on both sides to learn the secrets of the other via spies, and there were plenty of spy ops and counter spy ops in the world at that time. I would like to see some sort of way to mimic some of that in this game.