I would expect that some of the predicted effects of a "nuclear winter" would start to appear after a series of forest fires--albeit smaller in scope and intensity--but AFAIK this is not the case. What gives?
Most forest fires don't create strong enough firestorms (if they do at all) to funnel material high enough to have an effect -- most of the ash falls back down in a matter of weeks (even sooner if it gets rained out of the atmosphere). I'd compare nuclear blast firestorms with volcanic eruptions -- we do have a record of eruptions funneling material high enough into the troposphere and stratosphere to have a noticeable, longer-term effect on the climate (over the subsequent months and years).
