Any heating or cooling device that moves large volumes of air will also circulate particulate matter. That's why air filters were created. As for a wood stove sending dust into the room--none that I've used had this problem--even while cleaning. As the ash is being removed from the stove, there is a constant updraft from the chimney flue that draws the dust up the chimney--even when the stove is cold. And, because the newer stoves, which have catalytic converters installed in the stack is so efficient, much of the ash is incinerated, leaving very little ash to remove from the stove.

Cheers,

Gary