> bombs targeted on cities and industrial areas would start firestorms, injecting large amounts of soot into the upper atmosphere, which would spread globally and rapidly cool the planet
This makes some assumptions about how nuclear weapons would be targeted and detonated, assumptions which may not be correct.
Countervalue vs counterthreat targeting has been a back-and-forth for a long time in nuclear strategy discussions. The Nature paper relies on an assumption that there would be significant countervalue targeting—i.e. targeting cities and population centers rather than strictly military targets. This may not be a correct assumption about how U.S. and Russian nuclear weapons are targeted.
Second, the way that nuclear weapons are detonated has implications for the amount of burning and ash. Detonating weapons at ground level would limit the radius of destruction and increase the longer lasting fires burning the cities and projecting ash upwards into the atmosphere. But this isn't how nuclear weapons detonation has been modeled, pretty much since the Manhattan Project, because scientists realized that the shock of the detonation would destroy a greater radius if the nuclear weapon has detonated in the air above the target. This increases the radius of destruction, but decreases the long-lasting fires and ash projection upwards. Obviously it's not eliminated, but there is a significant difference depending on the manner in which the nuclear weapons are detonated. Both the U.S. and USSR have understood this.
While an all-out nuclear exchange that employs countervalue targeting against cities and detonates nuclear weapons at the ground level could result in what the Nature article models, that is an unlikely scenario given what we know about U.S. and Russian thinking/targeting/strategy. More likely is 1) not a full exchange, 2) counterthreat targeting, 3) detonation above targets. This will still result in ash, and fires, and destruction, but will be substantially different in overall outcomes.