During the First Gulf War, the uncontrolled oil fires in Kuwait were burning at a rate equivalent to 30% of all US consumption. Nothing remotely resembling a climate apocalypse occurred; major volcanic eruptions have far greater effects. Empirically, it seems highly improbable that repeating that experiment on modestly larger scale will unleash a global apocalypse. It isn't a convincing argument based on the evidence.
The above-ground petroleum storage facilities only hold days worth of oil that we are going to burn anyway.
But from what I understand, the crucial difference between the two models was how high the smoke would go, and as such the gap between the two models is actually a lot closer than the outcomes would imply. Had the conditions (weather, geography, etc) been ripe for more "self-lofting" of particulates, far more of them may have made it as far as the stratosphere, at which point they would stay in the atmosphere for far longer and would spread much further, without any weather patterns at that altitude to accelerate their return to the surface.
Seems from the petroleum front it's likely to actually reduce particulate matter over the course of months due to the lack of human industrial activity on the planet.
A limited nuclear exchange between RF/USA could extend to all large munitions stores, rocket stores, and petrochemical stores. All stores of nuclear launchers, warheads, and supplies intended for strategic war could be targeted.
Imagine all significant above-ground petroleum storage in RF/USA - large petroleum producers - is ignited. All counterforce sorties against targets near wooded areas will result in large forest fires.