I agree that halters shouldn't be left on for a long time. However, when horses are being turned out for part of the day, which many stables do, they will leave them on.
As for the horses nipping and kicking at each other, I'm going to assume they are geldings since mares don't usually do this. They are just playing. Two of our boys nip at each other all the time and they are best buds. They really get into in when the weather gets nice and in the spring. We give them orange cones to play with and that has helped. There's a saying that fits here: " Boys will be boys."
If it is just at feeding to though, they are probably acting aggressive and trying to protect their food or get the others food. At that point, you should step in and correct their behavior.