I don't think there is a thread on here about this (sorry if there is) so here goes! This isn't specifically for a story or anything- just interested by the idea.
I don't think it is possible for an equivalent to The Cold War to have occurred in the Wizarding World. Grindelwald was single handedly defeated by Dumbledore, whereas Grindelwald's equivalent (approximately) Hitler was defeated by the combined forces of USA, Russia and Britain (this is very simplistic but roughly speaking).
By having Grindelwald defeated in 1945 JK seems to be implying that events in the Wizarding world had rough parallels in the Muggle world. I've read journalist columns comparing Voldemort's rise to power, and the reason the HP books caught the world's imagination so much, to the rise of fundamental Islamist Terrorism.
However (sorry getting off the title thread) the Cold War dominated world events for so long, that the idea the Wizarding World's history could approximately follow/ parallel it seems silly.
Also (and I'm really hoping Tim will have some interesting things to say about this) how far would Wizards be able to interfer in Muggle events? Like would a Wizard in Germany in the 30s/40s who allows the persecution of Jews feel guilty in the same way as many German Muggles did and do?
Also would great social upheaval in the Muggle world (e.g Russian Revolution) be noticed by the Wizards, or have some rough equivalent? Considering Muggle inventions (like the Wireless) filter into Wizarding life, surely different political ideologies would as well?
And (thought of another one) the Statute of Secrecy was in 1692- therefore Wizards co-existed with Muggles during the English Civil War. WOuld they have taken sides, or just ignored it? Does this mean it is possible for figures from Muggle history to have been witches or wizards (meaning not just "official" wizards like Merlin or man I can't remember the name of who was Elizabeth's magician (when I do I'll edit it in)?
I'm sure there are similar things but that's all I can think of for now. Hope that makes some sort of sense. Any thoughts?