According to ancient urban legend, the .32 Winchester Special was intended to be reloaded with black powder. Factory ammo was loaded with smokeless, same as the .30-30, but Winchester knew that a lot of folks would reload it with black powder, and so the twist of the barrel was made with this in mind.
I can't (and won't) say this is true, but it makes some sense considering the times. Smokeless powder was the new thing, and not commonly available for reloading. My Grandfather reloaded his 12ga with DuPont "bulk" powder, a "semi smokless" powder that resembles oatmeal flakes. It smokes more than "modern" smokless, but has less smoke and fouling than black powder. I still have a handful of his shells!
Again, urban legend, but my own experience bears it out, that the .32 Special bores are marginal for accuracy. Fine when new, but often going "bad" with little or no visible wear to the rifling. Unlike the .30-30, which often seems capable of decent hunting accuracy when so worn one wonders if there ever was rifling in the barrel at all, the .32 just seem to go sour when it feels like it. Some believe this is to to the twist of the rifling, which is supposed to foul less when shooting black powder. I know that other .32 caliber rounds do not have any reputation for doing this, so one has to wonder. In a rifle like the Winchester 94, which generally are not shot a lot, many years of good service can go by without any trouble, and I think that's what Winchester counted on.
My father hunted with a Win 94 in .32 Special for well over a decade, seldom shooting even a full box of cartridges a year, and only shooting factory ammo. Then one season, when checking his sighting, his rifle would not group. Couldn't even get it to point of aim at 50yds, for no apparent reason. Still shot 6" low, with the sights adjusted as much as they could be. And I have heard similar stories from other people.
Can't say it's true, and I won't say it's not, but there's been talk!
Black powder in any cartridge will perform as well as black powder can, if proper loading procedures for black powder are followed. It is totally safe, again, as long as the right loading process is used.
Firearms designed for smokeless powder (primarily semi autos) will not function normally when fired with black powder, but they will shoot. Black powder will gum up the mechanisms in short order, and usually does not provide the correct recoil pulse to operate the mechaisms (and never with gas operated systems), so semis become instant manually operated repeaters, until they get too fouled even for that.
Small bore cartridges will suffer the greatest loss of performance, as no matter what you do, black powder velocities will only be between a third and a half of what the normal smokless powder load delivers, with concurrent loss of energy and change of trajectory.
jacketed bullets will change their performance radically as well, because the expansion is designed around velocities that black powder just cannot produce.
The exception are those rounds which were originally loaded with black powder (the "old west" rounds, like .45-70, .44-40, .45 Colt, etc) which are today loaded with smokeless to the original black powder pressures and velocities. Load these with black powder and you lose very little, if anything. You just have to clean them a lot more, and more thoroughly.