Well, I've been doing research on the bit ( it looks somewhat like http://cotswoldsport.co.uk/shop/images/loztomthumb.jpg with a chin-chain and whatnot ) and have come to the conclusion that I believe it's a version of a Tom Thumb. I'll get pictures up to be certain, but I'm quite sure. In digging, I found this is practically a universally hated bit which, in the wrong hands, can apparently make a horse have a hard mouth. I'd never really looked into them before despite usually going with snaffles, but I realize now that this may not be the best bit for her.
The owner before me was a younger girl, but one who was coached and very rarely left the ring. She said Willow was a perfect Western horse, and she is, though she responds much better to an English rein. With that said, I have a feeling the previous owner used a strong bit because Willow is a very forward, dominant little mare. If you don't have full control, you might as well not have any. She's pushy, but only really while riding and, when she hunkers down and decides against what you're telling her to, it does take effort to correct it.
So, my dilemma is this; should I try switching her to a snaffle and see how it goes, or continue with the bit she's familiar with?
If it's relevant, also, I usually just do western pleasure. May try barrels and such for fun, but I'm very much a trail gal. C: