I'll have a bash.
You could maybe think of it like this:
It's a bit like a copy - paste job.
Using the Pyramids of Mars as an example, The whole series of events occurred with the Doctor and Sarah Jane there.
But they weren't there until they were there. If you get me. They were pasted in from outside that series of events.
If you think now from the point of view of people in 1981 and beyond, the world didn't end (obviously). What happened was- Some god was re-awoken and tried to destroy everything, but the Doctor arrived and sorted it all out.
Until the Doctor arrived and sorted it all out, he wasn't there to sort it all out, therefore until he DID arrive, the course of the events followed to the destroyed earth of 1980.
While still in the process of sorting it all out ( the 'copy' had been pressed but the 'paste' hadn't been done yet) that was still what happened. (the earth was destroyed). He had to complete the 'paste' before the destroyed earth of 1980 had been 'cut', or 'pasted over' from the timeline.
I think in Cold War the Doctor must have known that events couldn't really lead to the nukes being set off, causing a 'hot war'. (Although there would be a very real danger of all that happened was the nukes malfunctioned and exploded, killing some marine life up at the arctic circle. The next day in the news the Russians might deny one of their subs was missing. Meanwhile in other news an unimportant earthquake was registered somewhere near the north pole.)
So there was still plenty of danger, although I'm betting he doesn't think the earth is going to be nuked from all angles. I bet he would STILL tell Clara and everyone else on board that the big danger was the whole earth being nuked as a result of this. The Ice warrior especially, as he already thought he had nothing to lose and might just kill everyone with his bare hands anyway. Him thinking he could work something out to take the world with him buys them all time while he sorts that out. The crew -so they would fight harder to stop the ice warrior and not give up hope that they were dead anyway. Clara -because the last time he let slip something of this nature to a companion, Rose nearly got both of them killed by time eating paradox things, when she saved her dad's life. (there's probably loads more examples, but this is the first that springs to mind). He wants Clara to be VERY careful with time and what she is doing in it. He probably also doesn't quite trust her yet ( he does take her to the haunted house next, with the alterior motive of having the psychic scan her).
So anyway- I think I confused myself somewhere there lol. Maybe we just aren't meant to know some of the answers to the riddles of the universe