The US/Russia/France have already detonated thousands of full power nuclear weapons all across the globe, primarily for testing. Although major cities would be ash, with millions lost in the senseless conflict, life would go on. You'd likely only have health problems if you had acute exposure to the blast. If you live somewhere irrelivant, radiation exposure won't be much more of a concern than it already is currently; whatever enviromemtal impacts nuclear weapons have, have already taken place.
Though the standard of living for survivors is sure to plummet, as famine and other secondary problems start to take precedence.
End of the world? No. Set back industrialized society two centuries? Sure.