Self carriage is a primary goal in dressage. When a horse is in self carriage, it is balanced independently of its rider, not using the hand or leg for support. You should be TESTING your horse often throughout your work. Learn how to do that here!
"Riding is, therefore, an ongoing, never-ending, challenging process. That aspect makes riding so intelligent and significant an effort. One merely strives, never arrives." ~ Charles de Kunffy
"If the rider encounters a problem, he must first look for the cause in himself. Most of the time, the rider is the cause of the problem. Only someone who looks at his own riding critically and is willing to improve constantly and learn more will be a good
Your balance and the strength of your core are what allow your position to be unaffected by your horse's changes of speed.
"The quality of a good canter: round, energetic, straight, cadenced, light. You have to feel in the strike off that the horse lifts his forehand without throwing himself forward." ~ Nuno Oliveira