The debris from the buildings both burning from the heat generated and collapsing from the explosive power the nukes is what sets off the nuclear winter scenario. Because nukes generate such a tremendous amount of heat over a very wide area there would be potential for a lot of very extreme fires, in addition to buildings (namely skydcrapers) collapsing and spew both ash and dust everywhere.

The sheer scale and destruction of a nuclear war would dwarf the last major conflict of somewhat similar scale. I really think you are underestimating just how much debris and fallout (radioactive or otherwise) would result from such a conflict.