In my humble opinion any Cold War game would require a system that differentiates thepolitical leanings of the population from those of the government and whether those leanings align to make influencing internal politics more exciting. It would also allow for more subtle tactics and make one's overall success or failure relevant.
For example: country A is communist according to its political pie chart, because communists constitute its majority if not its totality. The population is mostly communist according to its dedicated political pie chart, so there is an alignment between the government and the population and thus no trouble. Neighbouring country B is democratic as depicted by its own set of pie charts. As the decades go by, country B experiences economic growth, while country A experiences economic stagnation and, finally, regress. The political pie chart still indicates that the country is still run by communists and thus is still considered communist, but its population starts resenting its government (because, in their opinion, it does not manage the country properly), yearns for products and services available in the neighbouring democratic country (because the economy can't provide for their everyday needs) and is being influenced by democratic media and news or gossip coming from those who travelled there and came back (which slowly start seeping in as people look for some entertainment and wonder how people live in a different, perhaps even better system, and some of it may be part of a deliberate action taken by country B. Plus, it is hard to consider oneself a citizen of a successful country when children in country B play games on home computers and in your country having a home computer is considered a luxury if not a realm of science-fiction.). Thus, the political chart of the population starts indicating, that the population is drifting politically towards the democratic part of the spectrum, thus depicting its desire for a democratic government. The greater the disparity, the greater the chances that strikes, riots, and eventually, the formation of a political opposition, if not full civil war, will take place in country A.
This system would force the player to be mindful to not upset the population of its own country too much, making him or her make some hard choices (“Should I continue the Vietnam War and risk that my own unemployed citizens will turn against me, or should I end the war and stabilise the economy but allow Vietnam to become communist?”). It would also allow for a choice of strategies when influencing other countries. Feel lucky? Support a coup. The government will change and the population will slowly, but eventually follow the new system. Want to be subtle? Influence the population over a long period of time and make it do all the work of toppling its own government in favour of the one which is more suitable for your taste.
This system would also underline one of the key themes any Cold War must feature: in this war, everything is a weapon, not only the military. The more successful you are in fields of science, art, sports, economy, etc., the more people in the countries on the other side of the Iron Curtain want to live the way you do, because, obviously, your success did not spring out of nowhere. Outclass the oponent and, eventually, the hearts and minds of their citizens will flock to your ideology.