Anything is possible, but I have done, and been around a lot of black powder shooting during dry conditions, in grasslands, forests, and ready to harvest, or freshly harvested croplands, with only one incident.
That incident was the result of having read a magazine article in which the author claimed speedy reloading, and improved patterns in muzzle loading shotguns, by omitting over powder cards and fiberfelt wads, and using three crumpled Kleenex tissues instead.
Never checked the pattern improvement part, but those tissues would hit the ground smoldering on every shot, and did start a few tiny foliage fires.
The tissues were all we had along, so we finished our pheasant hunt with them, but we stomped out tissues on every shot we fired, plus a couple of small fires that day.
Otherwise, I have never encountered such a problem, but it is always on my mind when things are dry, so I do watch the ground in the direction of the shots, for a couple of minutes after shooting.
I would suggest not using full loads in the Dragoons and Walkers in dry conditions, because I have seen some smoke on the ground when I load my old Walker clone full.
Never noticed this with other cap and ball revolvers though, or had a fire start in front of them.