The reason people aren't reacting is because they don't believe the bluster, not because they're resigned to a slow death in an inevitable nuclear winter.
If the US military seriously thought the North Koreans were about to nuke an ally, it'd pre-empt that with conventional and/or nuclear means. And if POTUS were serious about nuking another country, I don't think he'd last long in office, let alone manage to carry out the act.
I'd be happy to bet as much money as I can muster as an indication of my confidence in our continued existence. Any takers? :P