I don't think it can be answered without something very simple: which actions? Giving Mosaddeq the boot in Iran? American support for the Shah's abdication and the effective surrender of power to Khomeini? The Iran-Contra scandal? Refusing to support Britain and France in the Suez Crisis? Refusing to supply Israel with weapons in the 1950s? Extending support to Israel from the late-1960s on? Basically, there's a lot of scope for policies when you look at the entire Middle East for the entirety of the Cold War, not all of which were the product of a single, coherent policy. Oh, a definition of the Middle East might also be helpful, as one could include gun-running to the Mujaheddin under definitions that include Afghanistan and Pakistan.
Actually, wait, no, sorry. I misread the question as American policy; my apologies. I suppose the question has to be revised slightly, though - which NATO policies? NATO conducted no offensive military operations during the Cold War, regardless of its military planning and defensive wargaming (*cough* Able-Archer), and regardless how some of its constituent nations acted; the first such action was the Gulf War, where NATO forces were deployed for a few defensive operations in Turkey starting in 1991 (AWACs to Konya and a full air defense package along their southern border), but I don't think that's what you're referring to. The first that was entered by NATO in full earnest after that was the Bosnian War, though, which is (a) not in the Middle East and (b) conclusively and decisively after the Cold War, so that's even less of a possibility.