Understanding your communication=happiness
Just because you put him in a halter that doesn't mean he is more happy. He may be more relaxed at the moment, but that may be because you aren't asking him to do much. Therefore he understands what it is that you are asking him to do, be it backup, turn left or right. But if you wanted him to side pass in a halter he may end up getting confused, frustrated with your signals, and that leads to unhappiness.
When you are sitting a top a horse, you are that much closer to God.