The horse needs to learn three things - lower her head to your request (clear to the ground if you ask it to by using poll pressure with your fingers - the key is to RELEASE the pressure the instant she gives any hint of lowering her head - slow but firm steps), flex (tuck) her nose in to your request as her head is lowered, and relax and flex (turn) her head toward you (with her nose tucked) when you are standing at the shoulder. Now, that's a simplified and quick description, but if the horse learns these three steps, you will have a much safer horse that is easy to halter. Once you are making progress with these three steps, make a point of removing the halter extremely slowly - make sure you can barely see motion as you lower the halter from her head. The horse will begin to lower her head as she follows the halter in anticipation of having you completely remove the halter. In reverse, she will also automatically begin to lower her head to put her nose into the halter once you have perfected the ultra slow removal of the halter. Sometimes I take a full 2 minutes to remove a halter when first teaching this to a horse. If the horse raises its head up, refasten the halter & get the horse to lower its head again in anticipation of having the halter removed then start the slow removal process all over again.
To be honest, it took me 2 years of watching my trainer friend work with young horses, haltering and bridling. before I finally figured out how she teaches horses to drop their heads and actually try and put their own noses in a halter.
My husband's Morgan will follow him all over the corral trying to put his nose into a halter my husband is carrying. The Morgan is actually insulted if my husband catches another horse and halters it instead. It's pretty funny to watch.
If the horse is lowering its head, but not tucking its nose, it is only pretending to yield to you. Tucking the nose with the head lowered indicates true submission. Yielding the head toward you, with the head lowered and nose tucked, while you are standing at the shoulder is a further indication of submission. Step by step, and always use pressure with RELEASE as the reward. Without instant reward (i.e., release of pressure) the horse has no reason to learn the step. This will all take patience and persistence, but the rewards for you and for your horse are immense.
I have also been taught by our trainer to keep my arm over the horse's neck as the halter is released. Not in an effort to muscle the horse - you can't win that kind of contest. I keep my arm lightly over the horse's neck, lower the halter all the way to the ground extremely slowly, talking & quietly encouraging the horse verbally, when the halter is off the nose let it slowly and gently fall to the ground, and make sure the horse continues to tuck its nose using pressure and release with your left hand. Praise the horse, stroke it on its neck with your right hand if you're standing on the left, and gently remove your hands - ONLY when the horse stands with its head lowered and nose tucked. The point of this exercise? When you do this properly, the horse will always amble away instead of suddenly taking off and possibly kicking you or knocking you over. My friend the trainer learned to do this when one of her horses whirled and broke her nose when she turned it loose the instant the halter was loose. My friend was just a teen when this happened, but she devised the above method to decrease the chances of the same thing ever happening again. This really works and I use the method with all of our horses, including my Arab. At first, the horse may decide to test you and try and whirl and run. If you hang onto the horse's neck and face for a few seconds, the horse will stop. Praise her! If the horse does not stop, you need to go back to your basic round pen training until the horse shows respect for humans as the leaders of its "herd."
Ellie May, I have to disagree with you about putting the halter on the horse as fast as possible. Slow deliberate movements are much more effective, but you have to do your groundwork before you can do any of this. Putting a horse in a corner only adds to the feeling that it is trapped, and you'll not get as much cooperation from the horse as you will with the groundwork.
Take time to put the halter on, take it off, praise the horse, put the halter on, take it off, praise the horse, etc. Don't tie the horse up, or work it - just teach it the halter isn't necessarily a bad thing, and that having it on doesn't automatically mean work for the horse. It's kind of like the first time you saddle and get on a young horse. That horse doesn't automatically know you aren't going to stay attached to its back forever. You have to get on and off several times to teach it to relax and let it learn you won't necessarily stay on its back permanently.
We have a Saddlebred mare we bought at age 8 from friends. This mare has a very, very strong flight instinct. I know her background and her training - she had never been worked in a round pen. She could never be caught before we bought her without using a bucket of grain, and she would whirl and run, as well as unexpectedly pull back sometimes when tied. Using the above methods, along with groundwork in the round pen took a few weeks, but she is now easy to walk up to and halter (I've never used grain to catch her), lowers her head and puts it into the halter, and no longer whirls and runs. She seems to have an area of comfort when tied to the trailer and does not pull back if tied near the back. Tied near the front and she occasionally has small panic attacks. Not ideal, but I will continue to work with her on this.
Good luck to all of you. I hope some of these ideas help.