The problem with the whole Star Trek WW3 scenario--and much of the assumption in this thread--is it's based on Cold War paradigm. But that's not how it's going to go. Or rather, the pop culture image of a swarm of arcing ICBM contrails and Roland Beyheimer style mushroom clouds over New York is mostly fantasy at this point.
Any coordinated existential-event level attack--either first strike or retaliatory--will be a panoply platform, where nukes are just one component. Most of the physical damage will still come from "conventional" missile salvos and the actually killing fields will come from chemical/biologics. In fact, it's likely nukes will factor very little in actually blowing shit up.
The whole of the post-industrial West/first-world/whatever-you-want-to-call-it is utterly dependent on electricity. [For more information, consult George Carlin.] As such, the most long-term damage potential would be from neutralizing a target's power infrastructure. And, while this can be done in part by directly attacking the power grid, much greater immediate damage can be achieved with focused EMP strikes at key breaking points. There's a lot of speculation (impossible to know since it's all classified, obviously) that a lot of the more recent weapons development (especially in China) has been focused on increasing the efficacy and range of EMP rather than doing actual damage. None the less, any attack against the United States or the EU or Japan etc. will be with the intent to disable the power network. Not only with this have immediate economic destruction, but it will make it nearly impossible to distribute emergency information or even govern.
This also have global implications. The biggest bugger about this electronics thing is how banking is done globally. And gold depositories really don't mean anything when global infrastructure is collapsing. More importantly, the key players (US, EU, China) in this theoretical event are all economic linchpins. The finical stability of all countries around the glob will fall like domino. There are only a few countries left in the whole world who aren't intrinsically dependent on the global market. No money means no governing. At that point the notion of "nations" becomes theoretical at best. Several will be able to hold it together for awhile--even a few years--but inherited tribalism doesn't hold a whole lot of weight when the sky if falling.
The next phases of an attack will focus on damaging fuel stores, water supplies, and transportation networks.
Next come the biologics, of which the US is particularly vulnerable. Americans exist in a near sterile environment because of everything from the fluorine in the water to the cleanliness of food to wiping the handle on your grocery shopping cart with a wet wipe. There's also antibiotics in everything. This sterilization collapses in a post-apocalyptic environment. For one, it becomes increasingly more difficult to create sustainable herd immunization because the baseline is so naturally weak. So, even if the biologics dissipate, there will a lingering vulnerability to naturally-born pandemics.
As far as other long-term effects famine is the other big one. Again, the US is particularly vulnerable because of the agro-industrial complex. While it's true the US produces a lot of excess foodstuffs, it's a bit misleading. Much of that excess is just byproduct. Crops are intentionally grown to produce over-yields. This is for a lot of reasons that aren't that important. But farms are able to do this because of how the system works thanks to both the technology and the economics (sic government subsidies.) You can do that, though when the technology is all borked and the economics of the government are essentially null.
Also, most of that over-yield is either corn or soy. Much of that is intended to be feed and not really edible. And even if it were, humans can't survive on corn and soy.
All that corn and soy in the US is grown in a crop-rotation cycle with wheat. This works great when you have the infrastructure, economics, and technology to support it. The problem is, once that stops, it becomes nearly impossible to grow anything.
Most of the farmland in the US is dying and is just limping along on the crop rotation system and the chemicals used to supplement it. The soil itself has become devastatingly nitrogen-deficient. While the soy and corn is still limping a long. It's causing huge problems with the wheat. This is why there's been such an increase of Celiac disease. It's not that people are just magically becoming allergic to gluten; it's that the wheat is now of such poor quality.
This is problematic when wheat is the only caloric-heavy crop you produce, especially when the population is under constant biological threat.
However, in other parts of the world, the wheat is of much higher quality. There's also rice and various other grains. The people growing them are also much more accustomed to and adaptable to traditional farming techniques. They also have much higher naturally immunities to protect from "dirty" crop yields.
As far as nuclear winter, that's not so much of a thing either. Or rather, the amount of fire-storm detonations needed to create the classic ice-age like conditions is completely unattainable-especially in the modern geopolitical climate. . More importantly, though. the effects aren't really localized. The real damage comes from the toxic aerosoled particulates that accumulate in the stratosphere and disperse across the glob. And, while they will have their own anti-greenhouse effect, it will only be a matter of a few degrees--which, ironically, will only be negated by climate change, anyway. So the most important thing to figure here is it will render higher altitudes nearly inhabitable. Which gets us to the heart of the matter.
With all nations falling, disease everywhere, infertile lands and large chunks of land inhabitable, humans will become mass-exodus migratory. This means that it's much more likely any would-be Zefram Cochrane would come from either the Amazon valley, central Africa or south-central Asia.
