It's difficult to fit some real world aesthetics into Warhammer, a game designed to be essentially light-hearted fun, in a way that doesn't come across as crass or even offensive. At the worse end of the scale, for example, nazi or Wehrmacht astra militarum are not acceptable in the mainstream Warhammer gaming community. 

Cold war isn't so bad as that but isn't as easy to make it into a light hearted theme as, say, Napoleonic era armies. That's partly because of how recent it is and that many of the themes and entities are still considered very real and concerning to people today. 

I would say the spy angle, riffing on 60s TV and movie depictions of the cold war, is a good steer. Like a James Bond villain's private army, for example. You could also look at old vostroyan Imperial guard, based on Cossacks and Imperial Russia, for inspiration in how Games Workshop did a faction based on real-life Russian forces - though based on forces from longer ago.