A hard mouth refers to a horse that has been subject to uneducated and abusive hand aids for an extended period of time and has become numb to the feeling of the bit. Some horses will even lean into the bit and pull against your hands. The effect of putting steady pressure against the mouth in this way is two-fold. As long as there is steady pressure, the horse is protecting himself against a sudden jerk, and also the steady pressure numbs the area.
Depending on the severity of a hard mouth (and to some extent the age of the horse) the mouth can be retrained to be soft (very responsive). The method of retraining would be the same as training an uneducated mouth. As stated in the previous article, it is important to be clear and consistent in your commands. Always starting with very light pressure and then apply stronger pressure until you get the response you are looking for. Training a young horse that is not properly educated to the bit is not a job for a novice rider. It is important that you understand how the other aids work in conjunction with your hand aids to communicate to the horse where and at what speed you want to go.
Steering can begin with proper ground work in making the horse move away from and yield to pressure. When I begin riding "baby" horses I ride with a halter on under my bridle and two sets of reins, one attached to the side rings of the halter, and the other to the bit. I have already schooled my horse on the ground to yield to pressure both from the halter and from pressure against the horse's side. Once mounted, I use my leg and the halter reins to tell my horse which way to go, and then I gently add pressure on the bit. I am very careful to be consistent -- leg, halter, bit -- for the first several rides. Gradually I start applying pressure to the bit and halter rein at the same time. After about a month or two I will gradually use less and less halter rein until I am riding completely on the bit.