Of course you can go to curb & back to a snaffle & so on, on a trained mouth. I can ride in whatever bit I want, even a spade if I so choose, because my horse's mouth is trained and so are my hands. I ride in a curb for showing, I have to. I ride in a snaffle at home, I sometimes ride in a kimberwick in english classes, just depends on the finesse I want. On a young horse, I would not do that, on a horse that has not given properly to the bridle, I would not do that, it's only basics, then on from there. On every horse I've owned, I've ridden snaffle, curb, you name it, once they are broke (broke, meaning resistance is broken, eg - they give to pressure).