A reminder for everyone: on this day in 1983, Stanislav Petrov saved the world.
It occurs to me this time around that there's an interesting relationship here - 9/26 is forgotten, while 9/11 is remembered. Do something charitable, and not patriotic, sometime today.
I'm assuming for your purposes that 1% of the population would have survived although I'm not inclined to actually believe that.
Yes. Humans would be much worse off. First of all, a lot of people would have died slow painful deaths. That's pretty awful.
Much of the nice spaces, such as areas where major cities are built would be unlivable due to the radioactivity. Many resources would be completely destroyed. Moreover there wouldn't be any infrastructure to use most resources. So anything in mines or the like would be inaccessible.
All the benefits of comparative advantage would be lost meaning that you simply couldn't produce large scale infrastructure and all the nice things we have. Similarly, medicine would go almost completely out the window. Producing antibiotics would be nearly impossible. Pacemakers and artificial hips and similar technologies would be nearly impossible.
The areas that will see the least change are areas like the deep Amazon or some of the less developed sections of Africa since they would not have had as many major nuclear targets. Life in those areas is pretty sucky even without a drastic increase in background radiation and the removal of all foreign aid. Even many of those areas have economic interactions with industries in the developed world.
Right. If anything you might get global cooling which is bad also. But this is a pretty silly statement. The scale of problems created by global thermonuclear war make the more worst case scenarios of global warming look like trivial inconveniences.