If you blow up all our nukes in the same place at once, you will make a bill hole and a hell lotta dust, but you certainly won’t destroy the planet or kill all life. In that case you might dessimate a lot of large animal and plant species. But there would still be survivors, probably including humans. Their lives would probably be miserable for a long time too. But anyway, we’re talking about climate change, not nukes, so I don’t get why you’re bringing that up?