There is some debate as to whether a nuclear war could be contained or whether it would result in what was once called "mutually assured destruction". The number of warheads currently in existence is still sufficient to precipitate a "nuclear winter" and perhaps result in complete opbliteration of all life on earth. The only way to prevent such an outcome is for all nations and individuals to have a firm commitment to peaceful dispute resolution mechanisms.

The implications of the sort of attack that you are mentioning would not be as grave as the consequences of a nuclear war would have been during the Cold War.  This is not to say they would not be grave, but they would not have the potential to destroy the whole world the way a nuclear war between the US and the USSR might have.

In the scenarios you mention, there would not be a war between two states with huge nuclear arsenals.  Iran has no nuclear weapons at the moment.  North Korea has few and does not have good systems for delivering them to distant targets.  Instead, what you would have is the US (or Russia, or Great Britain, or Israel) having to decide how much to retaliate against the country that provided a nuclear device to the terrorists.  Any of these countries could easily destroy North Korea or Iran without suffering much damage (if any) themselves.

Such an attack would lead to the deaths of many people, perhaps millions of people.  But it would not lead to a global nuclear holocaust.