So you think you can slow down a horse with a bit? This is a very common misconception about horses. Bits are not made to control a horses speed, a horses speed should be controlled through the seat and legs, but not the bit. Many people think they can slow down a horse with a harsher bit, but really this just makes a horse and more uncomfortable, and more likely to act out- bucking or bolting to escape the pain of the bit.
For example, do you know why race horse jockeys keep a firm hold on the rein and even during a race when they are trying to get their horse to run as fast as it can? Jockeys don't use the horses bit to slow them down, they use the bit to make the horse run faster! It's proven that a horse can run faster when they have something to lean in their mouth, like contact their reins and bit! If the jockeys were to drop the rein, the horses would not be able to run a fast. This is true of regular trail and riding horses as well, it is much easier for a horse to bolt and run away with a rider when a rider has a strong amount of pressure on the reins than when a rider has loose contact.
The better way to slow a horse down is using your seat and body and utilizing figures to get the horse more balanced. Many times when a horse is unbalanced the beat up, in effect trying to catch themselves as as they are falling -- like when a human starts to fall they may jog forward to catch themselves. To get your horse to slow down their gaits, simply riding them more frequently may help. This helps them develop the muscle they need to carry themselves and a rider safely.
One way to get a well conditioned horse to slow down is by a taking a deep breath out and sitting deeper in the saddle. (visualize pushing your seat bone or your tailbone deeper under yourself, or sitting on your "seat pockets"). Be sure not to grip with your legs when a horse speeds up. Many riders pinch with their legs when they become uncomfortable. When your horse speeds up, try turning your the horse to slow them down. Turn first with your body, looking where you want to go and then signal with your reins. It is much more difficult for a horse to move too fast or bolt when the horse is working on patterns and figures, so if your horse is too fast, keep them busy and balanced by doing figure eights, circles, serpentines, and other random figures.
Using a bit to slow down a horse is only acceptable in small increments. You should have contact when asking the horse to slow down, but you should not grab the reins tightly and hold until the horse slows. Instead, try gentle "bumps" on the rein to signal the horse to slow, along with your seat and body. This method prevents the horse from leaning on the bit and going faster. This is the only way it is "correct" to slow down a horse using a bit.
If you cannot slow horse down with a plain snaffle bit, your horse needs training, not a different bit!