What do you make to the argument that the probability of nuclear winter caused by climate change is considerably lower than the probability of nuclear winter, so focusing more directly on nuclear winter looks a better bet?
Of course it will be smaller, however that does mean that tackelling climate change will not make a sizeable contribution towards reducing the risk of nuclear winter. The question for me is whether nuclear winters that relate to climate change are more or less tractable than nuclear winter as a whole. My view would be that trying to reduce the risk of nuclear winter by tackelling climate change and its consequences may be a more tractable problem then doing so by trying to get nuclear weapons states to disarm or otherwise making nuclear war less likely in general, but that efforts to make nuclear winter more survivable are probably more efficient than either of these policies from a purely x-risk reduction perspective.
However, I also do not think that nuclear winter is the only way in which climate change may lead to an existential threat (at least reading existential threat to include the prospect for an unrecoverable from civilisational collapse) as there are some interesting feedback loops between environmental and social collapse that have the potential to cause non-linear and self-perpetuating shifts in the structure of global civilisation. Admittedly these are hard to study, but from a value maximisation perspective I would say that in the face of uncertainty we will do better if we assume that global civilisation is relatively fragile to such changes than if we assume that it is more robust to them.
I don’t agree that working on climate change is plausibly a better way to reduce the risk of nuclear war than working directly on nuclear war. Firstly, climate change is a very intractable problem in the first place for philanthropists and for national governments, given that action is opposed by entrenched interests across all society and requires cooperation pretty much of all nations. Nuclear peace is opposed by some entrenched interested in the military industrial complex, but these do not reach anywhere near as far into society as a whole. Major results could be achieved just by getting cooperation between Russia and US, which is not true of climate change.
Secondly, climate change is much less neglected than reducing the risk of nuclear war. Thirdly, there have been lots of apparently successful treaties that have e.g. limited the size of US and Russian arsenals. It just seems much easier to make progress on things that foster peace and reduce arsenals than on nuclear war caused by climate change. The path for the latter is extremely indirect.