I really don't get this question, if you would play any nation during WWII there is a big chance that there won't be any cold war at all. Ofcourse it's true that some events during the war triggered the later cold war, but being allies and fighting the bigger danger brought the opposites communism and capitalism closer together. Ofcourse after the war this impossible relation couldn't stand for a long time, but only then the cold war started. I really don't think that playing through a different era you could still trigger the events that lead to the cold war.
Also I don't think that you can trigger the end of the cold war to happen in 1989. Ofcourse it would be interesting to see what might happen post war, when the us would be more aggressive towards the soviet union and create the iron curtain instead of the russians, but maybe this will be possible to do with the eventually upcoming game Balthagor speaks about in the above post, but I would find it interesting to see what would have happened if the freed countries were let go, no warschau pact or nato was formed. What countries would lean towards the US or Soviet Union, would there still be enough influence across the world capitalist and communist wise to trigger the vietnam war or cuban revolution or would there have been world peace after all. When it comes to technology, we may not have gotten any jet planes or the man on the moon would still be a fairytale, not to mention computer technology or the internet.
If there was world peace countries wouldn't spend billions on defense budgets, so maybe we would have a cure for cancer and aids instead. I think this scenario would be real hard to think off, but if any game is capable of doing this it would be one of the paradox games, possibly a future supreme ruler game, but I guess these world events would be too hard to trigger, not knowing what would be necessary to get this new world order. My guess here however is that when communism would be allowed in the US and capitalism in the USSR, this may bring both superpowers closer together after WWII.