The snaffle bit works on several parts of the horse's mouth; the mouthpiece of the bit acts on the tongue and bars, the lips of the horse also feel pressure from both the mouthpiece and the rings.
While direct pressure without leverage is milder than pressure with leverage, nonetheless, certain types of snaffle bits can be extremely harsh when manufactured with wire, twisted metal or other "sharp" elements.
[2]: 79 Curb chains or straps have no effect on a true snaffle because there is no leverage to act upon.
While some riders in western disciplines do add a curb strap to the rings, it is merely a "hobble" for the rings, has no leverage effect and is there only as a safety feature to prevent the rings from being pulled through the mouth of the horse, should the animal gape open its mouth in an attempt to avoid the bit, an outcome prevented in an English bridle by the presence of a cavesson noseband.
[2]: 79 There are many riders (and a remarkable number of tack shops) who do not know the true definition of a snaffle: a bit that is non-leverage.