It depends. If there are nuclear weapons at play, then the whole world will lose, due to nuclear radiation. Would just be a matter of time. If not, most likely the US. But they would be the biggest target, so it's truly hard to tell.
The countries that are the farest away from the dumb guys bombing each other! I think most countries would get fucked. Especially murica! They have a lot of enemies and would get bombed from all of them and they would bomb back but the countries would lay in ashes from 0 to a 100 real quick!