I think it's more likely that free-floating nanobots would be swept away by the weather than have any control over it. Try filling the air with a cloud of nanites and they'd get washed away by the first decent rain. Try to keep them in a particular configuration and they'd get blown away by a gust of wind.
But if there were billions of them in the upper atmosphere, they could probably selectively adjust their density, reflectivity, opacity, etc. to block, filter, or concentrate sunlight in desired areas, affecting heat flow and large-scale weather patterns. You could cool a region down by dimming the sunlight, or focus or amplify it to accelerate a thaw, something like that. Or they could be used as nucleation particles to encourage cloud formation or precipitation, like real-life cloud seeding.
But if you're thinking about something like conjuring up a tornado or lightning storm at a moment's notice, that would never work in a science-based scenario. The processes that lead to such events happen on a very large scale over a considerable amount of time, so you'd probably need to start influencing weather patterns days or weeks in advance across a wide swath of the planet to produce desired weather conditions in a given area. And at most you'd be increasing the probability of the weather happening the way you want; weather is far too chaotic for results to be guaranteed.
If there were already a thundercloud overhead, it might be possible to line up a chain of nanites to form a conductive path for a lightning strike at a given point, or just build a high enough chain to act as a lightning rod. But you'd need to anchor them together through physical contact or some strong attractive force so they wouldn't get blown apart by wind or rain.