A snaffle is a snaffle because it isn’t a leverage bit. Any bit that has shanks becomes a curb bit (or leverage bit)- whether it has a broken mouthpiece (like a snaffle) or is a ported grazing bit. The reason for this is that a snaffle works on a direct rein and doesn’t utilize leverage.
There’s a correct and incorrect order in which to saddle your horse. When done correctly it will keep you and your horse out of a wreck. When done incorrectly, well, you might find the saddle somewhere that you’d rather not have it be.