I am not a professional trainer. My son and I train our own cart ponies, but I am no pro. I do, however know great tips which I have learned from others more knowledgeable than myself and tricks I've learned just from being around my horses.
When our first foal, Desi the problem child, was born we had no experience with foals. I'd worked with adult horses most of my life so I knew the best way to teach him to wear a halter would be what many people know as either "approach and retreat" or "pressure and release". Horses do not like pressure. The trick is to get them to understand that pressure is relieved when they give a correct response. When you have a frightened or unsure animal, teach him to accept the things that scare him by A. approaching him with the scary object a bit at a time and remove it before his fears overcome him. Each time you bring what scares him a little closer and remove it before his fear makes him move away from it. If he moves away from it, move with him until he stops and then take the scary object away. Finally, rub him with the scary thing until he stands still and is relaxed, then take the object away. This teaches him that if he stands still you will relieve the pressure of having the scary object nearby. and B. letting him follow the scary object as if it is actually running away from him. Heck, it must not be that dangerous if he can chase it away right? In these two ways you can teach your mini to accept just about anything. He learns to trust you and you learn the signs your horse gives you when he is worried, fearful and when he relaxes. This knowledge is invaluable to both of you for the rest of his life. He has to be able to trust you as his herd leader, and you have to be able to read the subtleties of his body language before he tramples you or jerks the lead rope out of your hand and heads off cross country without you.
When we halter trained Desi, he was already our little buddy and trusted us implicitly. We had been by his mother's side when he was born. I had my hands on him rubbing him before he was even fully out of his mother. I sat on the ground in their stall and let him come to me. I'm tellin' ya, the little man and I were close. He was two weeks old when I brought his little halter to him and his only reaction was to trot over to see what "granny" brought him to play with. I let him play with it. He chewed on it, tugged on it and stomped on it a couple of times just to show it who was boss. I scratched his itchy spots with it. The halter was his friend.
In the course of playing with the halter, I rubbed his face and ears with it, put the nose loop over his nose, removed it and moved on to rub his neck. I put the nose loop over his nose several times, always following that with more rubs on the neck with the halter. I put the loop over his nose, the strap behind his ear, held it there for a second or two, removed it and rubbed him with the halter. After about 20 minutes I put the halter on him buckled it and rubbed his neck and scratched his mane while he tried to figure out if he could lift his head with this thing he suddenly had on his face. He pawed at it a couple of times but as soon as he was relaxed and enjoying the heck out of the attention he was getting I took the halter off.
We'd play his halter game several times a day for a day or two and let him follow us around wearing it. When we were done with him we would take it off. NEVER leave the halter on your horse, especially not a foal. Halter buckles can easily get hung in fencing when the horse is rubbing it's head. A foal can hang his tiny hooves in a halter that is even slightly loose. As you progress in the training of your horse, the halter means he must pay attention, no halter means he's done a good job and is being rewarded with time off. You don't want to go out and find your horse has strangled himself or broken his neck because his halter buckle got tangled in his fencing.
Yeah yeah, I know "He's easier for me to catch if his halter is on!!" Teach him to catch you. Even if I could run, I couldn't get away from most of my miniature horses. I'm the best entertainment they have. I'm their mini-horse version of PBS. I do cool stuff, I'm fascinating, and I scratch their itchy spots. I bought a little ranch horse several years ago that had been used as nothing more than a ranch tool his entire life. He had no clue that people were interesting. He was just caught, saddled up and ridden out to work. He was an extremely trustworthy mount, well trained, well behaved and had his needs cared for, but he did everything with a fairly dejected air of submission. Haltering him was an exercise in frustration. I'd go to his stall and he'd put his nose in the furthest corner. He never ever offered to kick or muscle past me, he'd just calmly step away. Once I'd finally get the lead rope laying across his neck he'd stand still as a stone for the halter. It was just getting close enough to get the lead rope there that was the pain in my neck. A friend of mine in California came for a visit and, as she is excellent with horses, she came out to see my new prize. She taught me a trick that I have used on every horse since. She calls it "The Jellybean Game".
You don't need jellybeans really to play this game. You can use rocks on the ground, a piece of a stick, you can even use a good book. You put your horse in a round pen or small enclosure where he can stand at least 12 to 15 feet away from you. Far enough that he's more or less "free" but close enough so that he has to notice you. Then, you sit inside this enclosure and pointedly ignore your horse. My friend counts jellybeans. I play with rocks, scratch in the dirt with a stick, or read quietly. Horses are incredibly curious. If you play that curiosity right, you can teach them almost anything. She and I sat in the dirt of a round pen and ignored my ranch horse. Within 5 minutes he was standing within 4 feed of us, craning his neck to see what we were doing that was more interesting than him. 5 more minutes passed and his nose was in the middle of our business. We'd reach up and rub his legs and chest from time to time and go back to ignoring him. Within 20 minutes that day, without handing him treats, chasing him down, following him around in frustration, we taught that little horse that people are actually kinda interesting. From then on, I'd open his stall door and he'd amble over for a neck scratch and his halter.
This same thing works for minis. You'll find that if you even go out to fix his fencing, or clean out his water bucket, you're so darned fascinating he's going to come over to supervise. Patience is your task to learn. If you have to catch your horse in a large pasture or paddock, you will need to wait him out at first. Make enough noise while pretending to be doing something that doesn't involve him that you capture his attention but not so much that you frighten him away. It may take some time if all you have is a 200 plus foot pasture, but eventually he will come. Try different activities to capture his attention. Don't just grab him and halter him when he finally ambles over to see what you're doing. Scratch his itchy spots, pull up some grass and offer it to him, and pay only enough attention to him to keep his interest and keep him close while you pretend to be interested in some very important chore, rock, jellybean or book. When you have him coming to you easily, then put the halter on him. This process may take a day or two with an adult mini who has a larger world view, but to a weanling you ARE his world so this will take a very short time.
Yes, there are other ways to do this by working the horse (applying pressure) until he is facing and paying attention to you and "hooked on" to you, but I have a hard time walking so it stands to reason that I should make a horse with 4 good legs do the walking while I just sit and become more fascinating with each passing minute.