It is not as simple a 'soft hands' and 'hard hands'.
It is a matter of 'good hands', 'good feel', 'good timing' and 'good control' of the rider's hands. Hands need to 'soft' when the horse is responding correctly and need to be 'effective' when the horse is not so that they educate the horse's brain (not his mouth) to respond to the lightest contact.
If I have a horse 'lean' or 'push' against my hands I get pretty harsh with them and drive hard with my legs and take a hard hold on those reins. Withing a few minutes, the horse will become desperate to get away from my hands. He usually first will raise his head. If the rider's hands pull even harder, the horse will probably sling his head from side to side to get away from the rider's hands. If the hands are still there and the rider's legs push him even harder into the pressure on his mouth, he will finally 'break at the poll' and bring his mouth down and back toward the rider's hands.
BINGO! If the rider gives him release (relief) when he does that, he will quickly learn that it is pleasant when he gives the correct response and not-so-pleasant when he pushes against or fights the rider's hands.
If a rider just engages in a pulling match with a horse, the 1000#+ horse is always going to win.
We don't train the mouth -- we train the brain. We make it unpleasant for the wrong thing and comfortable for the right. So, if a person never pulls hard enough to make the wrong thing difficult or unpleasant, the right thing never happens.
The rider should strive for 'good hands'. These are hands that makes it rough on the horse when the horse does not do the right thing and are soft and kind when the horse is doing the correct thing.
After only a few rides, any horse with a trainable and cooperative mind should be able to be ridden with the reins lightly held between the rider's thumbs and pinky fingers and should do downward transition and stop with only that much hold of the reins.
Once the horse's mind has figured out that you intend to reinforce the request made by way of the reins, he will simply have more respect for your hands. Then, the kind of response that he is giving you when you give him release (a light hand) is what you are or have been training him to do.
To have 'effective hands', you have to take more hold when it is necessary and give release and ride with a light hand when he is responding correctly. Then, on top of that, you need to learn to ride with 'perfectly quiet' hands that do not bump and jerk the reins as you ride. Most people have hands that move a lot more than they think they do. Videos of one's self are an excellent tool to use to determine how 'quiet' and 'steady' one's hands actually are.