I agree with everyone else here. Halters should be left OFF if at all possible. There is always the risk of a horse getting caught on something and injuring themselves, even if they won't be unattended long, and even if they have a breakaway.
Last winter, when the weather was bad, my grandfather turned my mare out in the riding arena while my dad cleaned her stall. It was a chance to let her stretch her legs since the footing was not safe in her pasture. He left her halter on as he was planning to stay with her and watch her while her stall was being cleaned, and then bring her back in. Well, the bedding delivery truck came while he was watching my mare. He stepped away for less than five minutes to say something to the delivery truck driver, and in this time, my horse reached her head under the fence and got caught. She was wearing a breakaway but with the angle of her head and how she was caught, the crown piece didn't break. He returned to find her straining and struggling. She broke the piece of wood she was snagged on before my grandfather could try to help her. Luckily she was okay. Her face was tender for a week or so afterwards but no serious damage was done.
We all learned the hard way that it doesn't matter if you're nearby, or if the halter is only going to be on for a few minutes. If a horse can get themselves into trouble, they might find a way! It's not like the fence was in bad condition either. The arena fence was less than a year old at the time.
Also, consider the design of a breakaway halter. The horse has to be straining against the crown in order for the breakaway strap to break. If they are struggling side ways or if their head is pinned to the ground at an awkward angle, they won't be able to free themselves in a breakaway. Even if they do break the crown piece, consider the strength of that strap. A horse has to pull pretty darn hard to break that leather, and they can still injure themselves even if they do manage to free themselves.
If your horse is not totally wild, but just tough to halter, leave the halter off and confine her to a smaller turnout area until your horse gets used to being caught.
My horse used to be a pain in the butt to catch and now she's easy to catch. Here are a few tips that might help you get your horse to cooperate with being caught:
1) Don't always work your horse after catching her from the field. Sometimes just catch her and let her go again, or just bring her in for a grooming and let her go again.
2) Check the fit of your bit and saddle. If your horse is uncomfortable during her workouts, your horse may be less eager to be caught.
3) If possible, make sure all of the horses are brought inside to eat. If your horse doesn't allow herself to be caught, all the other horses come in and get fed, and she only gets to come in and eat when she cooperates. Food motivated horses will hate seeing the other horses get brought in and fed first and will quickly change their behavior.
4) If you are approaching your horse with the halter head on and raising it up to put it on, try a less aggressive approach. Approach your horse from the side of her neck. Put the lead rope over her neck so you have some control and put the halter on while you stand on her left side, facing forward. Use your right hand to bring the crown piece up over her ears and your left hand to guide the nose piece around her muzzle. Be gentle, speak kind words, and stay where your horse can see you.
5) Consistency is key! Keep working with your horse and be consistent! Don't give up and have patience! Your horse will learn to cooperate someday if you just hang in there!