Halters come in basic shapes and a few different sizes, but the colors offer each owner a sense of uniqueness for their horse. Halters are made of fabric like nylon or leather. Halters do not have bits and therefore do not offer the control that a bridle does, it is not recommended that your ride a horse with only a halter.
A halter consists of a noseband and headstall that buckles around your horse's head enabling you to tie him up or lead him. Lead ropes are connected to a metal ring on the halter. Halters fit looser than a bridle, but there is still the possibility of the skin being rubbed by the fabric.
I really see no need to leave a halter on a stabled horse unless he is green or very young. A horse used to being handled is easy enough to approach in a stable to have his halter put on and taken off when needed.
If your horse lives out in a pasture you may benefit by leaving his halter on him, but it honestly does not help your horse. Your horse may be easier to catch, but the chances of him getting his halter caught or snagged on fence post or tree branch is very likely.
If you turn your horse out on a daily basis for a couple of hours with his halter on there is still the risk of injury. If you leave your halter on you should buy a break away halter that way injury is prevented and you won't have to blame yourself.
It is important to check that your halter fits your horse properly and is cleaned regularly to remove dirt. Tip: When putting your halter on your horse there should be enough room between the throatlatch (usually the part that your buckle up) and the horses jaw - room enough for a hand - to make sure that it is neither too tight nor too loose.
Every horse owner would be wise to invest in two halters so that you always have a backup if one is broken. Halters have metal fastenings, but this does not make them indestructible. I was once grooming a horse in her stall, she was a feisty mare, yet somewhat insecure and pretty fussy. I had her secured to a ring by a short lead rope.
One minute I was brushing her body and the next minute we had both jumped and spun in her stable. Who knows who reacted first, but I do know that she had gotten a fright and broken free; the metal ring on her halter broke in her hasty and abrupt movement. Did I have to waste time searching for a halter in the owner's yard, not to mention the worry over having to explain how the halter got broken...
Always buy a good quality durable halter and have another for backup. Remember it is not what the halter looks like that counts, but that it works for you and your horse. You really do not need that beautiful flashy leather halter if your pocket can only afford a standard nylon halter.