Quit with the soothing reassuring mindset. Only makes a horse worse.
Be very matter of fact, low tone of voice, and don't draw words out either. Keep chatter to minimum, just what is needed to get job done, and don't pat/praise, just get on with program.
Doesn't matter what type of halter as much as what type of handler. I've used nylon, rope, leather, and even in a pinch clothesline, belt... or bra. Don't ask. Long story.
Anyway. Point I am making is this. The person on the other end of the "attachment" plays a bigger role by far than the gee gaws used. How you walk, how you move, how you respond will tell horse that YOU are the leader, and that YOU have everything under control.
Horse may still look around but will not lollygag.
I agree with most of what Saddlebag wrote, with the exception of the placing of hand when leading. The vast majority of the problems I am seeing with horse owners lately, is that they want to keep hand by their body rather than up by the halter ring where lead rope is clipped.
I lead, and teach to lead, with hand under horse's chin at clip, so that corrections can be made if needed quickly. I kept wondering why people were having their horses waller all over the place, even when horse had started out at throatlatch/shoulder, and finally figured out it was their hand placement. Arm is extended out from body to halter/snap, both to keep horse off me, and to give me heads up when horse is not in tune with me.
Horses make me a better person.