First of all, the so-called nuclear winter effect is likely considerably overstated by the TTAPS Report, and probably massively so. A massive amount of particulate matter in ejected from the surface into the atmosphere would naturally precipitate out by both nucletion of atmospheric water and natural convection within a relatively short period of time (1-3 years). This would certainly have regional, and perhaps hemispherical affect on sunlight and temperature, and would likely be devestating to agriculture in the short term, but not quite the decades-long cataclysmic result banded about by nuclear winter adherents. The analysis on which the report was based used a number of gross simplifications due to the limited computing power available at the time, and the homogenetity of these assumptions, combined with a lack of consideration for complex climatological effects gives an impressive but unrealistic worst-case answer.
Carl Sagan, one of the authors of the TTAPS Report, used these results as a basis for his claim that burning fire wells in Iraq after the first Gulf War would cause regional ecological disaster; the results, while palpable, were far less dramatic than his claims, which he later publically acknowledged; nonetheless, the meme of a world-destroying nuclear winter remains in the public consciousness.
Note that this doesn’t have any bearing on the detrimental effects of residual radiation, both from fallout residue and activity of fissionable materials via fast fission, which in any wide scale exchange would have resulted in long term hazard that makes Chernobyl look like a wet noodle. So, nuclear winter aside, there’s still plenty of good reasons not to go about lobing nuclear weapons at one another casually. (Presumably, if one deliberated the decision to engage in nuclear warfare one would find good reason to desist at all, but such decisions enforced by the idiot logic of game theory and strategic Assured Destruction are relatively innured from deliberation and rational thought.)
So this business about a one-time injection of solid particulates residing in the atmosphere for “years” is hyperbole. But for the sake of the o.p.‘s question, what about the case that some kind of convection layer kept material suspended, or material were continuously ejected into the atmosphere. Because eletrostatic attraction drops off proportional to the inverse of the square of the distance between charges, you are either going to have to have a really honkin’ large attractor or a hell of a lot of them, and of course, as you accumulate particles they’re going to neutralize your charge, so either you have to have some way to capture and filter them out, or your attractor has to be disposable. You’re also going to have to make sure your ionizer is the opposite of the net charge of whatever you’re trying to attract lest you just disperse it further away. It’s relatively easy to come up with some kind of conceptual method of making this work; in practice I think it would be problematic at best, and would take an enormous amout of energy.
Oh, and don’t expect to get anything factual from the Discovery Channel. When information presented there intersects with reality it is purely incidental.