Agreed. It's hard to see any way that New Zealand, just as an example, could have a decisive influence in a USA/USSR generalised nuclear conflict. No matter who "wins", they're in appallingly bad shape even if no warheads land within 1000km of the shore. NZ depends on a wide variety of goods that are only made overseas (example: ball bearings), and a nuclear war will play hell with global trade routes. I have a book called "New Zealand After A Nuclear War", published by the New Zealand Planning Commission in 1987, and the picture it paints even in a scenario with no strikes in NZ is pretty grim.
There's also the fact that it's not enough to just have nuclear warheads, you also need delivery systems to get them to their targets. Not all of the nuclear weapons available were on platforms that could reach any part of the globe. An ICBM that can reach New Zealand is also able to reach the missile fields of North Dakota, and there aren't really all that many such missiles. This goes double if you want to assign more than one warhead to some of your targets, as would undoubtedly be the case.
Many of the Soviet warheads were on IRBMs or as weapons for bombers, and many on both sides were "spares" - not actually mounted on a delivery platform, but intended for reloading platforms that survivde the initial exchange and made it back to rearm.
Teal deer version? Many of the nukes aren't on delivery systems to start with, many more can't reach these minor targets, and there's not much in the way of reasons for attacking them anyway. I'm not saying it wouldn't happen, but there's an opportunity cost of sorts associated with attacking places like that.