I just want to "throw it out there" that using a snaffle may not always be the answer to getting a horse softer.
For example: Right now, to get this horse to stop, you must pull, pull, pull until she stops. You're having to use quite a bit of pressure to get that accomplished. However, what if you put something on her with a short shank? That would allow you to barely pick up the reins and BAM she stops instantly. Yes, you've moved onto a "harsher" bit, but really .... the harsher bit is actually softer, because you barely have to apply any pressure at all.
Just a thought, anyway. (Of course, the "harsher" bit has to be used correctly 100% of the time, or you will cause the horse to eventually ignore that too)
Another example: I rode my horse Red in a snaffle (mostly) all summer last year, trying to get him softer after I bought him. We didn't get as far as I wanted. So to get some help, I have him at a reining trainer. Guess what she's working him in right now:
And he's responding beautifully. Bending, flexing, and giving nicely.
So anyway, just wanted to say that a snaffle isn't always the answer.