Answer:
This is a very common riding fault and is usually seen in new or inexperienced riders. It's natural when we feel insecure to 'grab on' for dear life. As our riding improves so should our hands. A good solution is an 'Oh, my!' strap. A short strap attatched to the front of the saddle or a breast collar make a perfect place to hang on until the time when the rider's balance and seat are more solid. It is also perfectly respectable to 'grab mane' when the need arises.
Another way to encourage soft hands is to drop the reins and have a friend work the longe line while the rider uses just seat and legs. This will help with the rider's balance and build confidence at the same time.
While working on the soft hands it may be a good idea to work without a bit so the rider doesn't bump the horse's sensitive mouth.