I've worked with a lot of different kinds of horses over the years, used in quite a few disciplines, and employing an array of diverse gear. Often I've noted that excessively complex, redundant, and unneeded tack was used out of tradition, ignorance, or an attempt to find a quick fix to what really called for better horse training or horsemanship.
Probably the worst were the polo players. You'd see miles of strap on their critters... Once saw a horse wearing standard and running martingales, bit and bridoon style bridle, but with a pelham and double twisted gag bit, with the double reins from the pelham, another rein from the gag, and running side-reins through the snaffle ring of the gag, all in use at the same time! I worked the same horse in the off-season with a low-port cutting horse bit and a simple one-ear headstall.
So I used to look at the carriage horses, with all their harness strap running every which way and buckles all over the place, and figured that most of it was just for tradition or show. Surely a much simpler rig would do the job as well!
I was half-right. Farmers often do use a simpler form of harness... But only for drag loads. When it comes to pulling a cart, wagon, or many other implements, all those bits of harness serve important purposes.
A quick aside to consider the different harness materials...
Leather is the traditional harness material, and many swear by it. It does tend to be horse-friendly, but it's relatively heavy and takes more work to maintain. Being a natural material, it's strength cannot be guaranteed.
Nylon is very popular these days. It is inexpensive, very strong, light, and easy to clean. It is also available in showy colors if that's your thing. It can rub and chafe horses though, so other materials are often employed at at pressure spots.
Biothane is nylon coated in urethane plastic, It has nylon's strength, smooth surface to reduce rubbing, and generally resembles shiny patent leather. Won't absorb moisture like regular nylon, but can be a bit stiff and sharp.
Betathane (or Beta) is nylon coated in a softer urethane that looks and feels like harness leather, but retains the strength of nylon. Not quite as resistant to scratching and surface damage as biothane though.
The traces are the thick straps that run from each side of the breast collar or hames back to the singletree. Cart harnesses often have the singletree ends of the traces with a loop or slot for attachment, while pulling and draft harness traces end with a heel chain which allows easy length adjustment at the singletree. The traces bear the full strain when a horse pulls a load forward, so strength is important. Even teamsters using full leather harness sometimes prefer to switch to nylon traces.
If a horse is going to be used strictly for pulling drag weight (walking plow, stone boat, etc.), little more than a collar, hames, and traces are needed. Perhaps a strap over the back keeping the traces out from underfoot when slack. But for any kind of a freewheeling load employing shafts or tongue, a full harness is called for.
The opposing part to the collar is the breeching. Basically a strap that goes around the back of the horse's rump. The horse can slow or stop a load by sitting back against the breeching.
A surcingle, composed of a wide back band, belly band, and billets, goes around the horse's torso a bit behind the front limbs. When a horse is hitched single between shafts, this surcingle holds up the shafts and pulls them into turns. The back band also provides guide loops for other rigging, including line rings in breast collar harnesses.
Top (or back) straps run from the top of the breeching harness, through loops in the back pad, to connect to the hames, holding the whole harness together on the horse.
The breast strap attaches to the hames in front of the horse, with its pole strap running between the front limbs and slipping under the belly band. Quarter straps run from each side of the breeching to meet under the horse's belly and attach to the pole strap. When working in a team alongside a tongue, the horse's stopping power is transmitted from the breeching through the quarter straps to the neck yoke via the pole strap.
The crupper is a rolled strap that passes under the dock of the horse's tail. It is sometimes omitted in full harnesses. Due to the light weight and flexibility of nylon harness, a crupper is useful for keeping the harness centered on the animal's back.
The driving bridle is similar to a typical brow-band style riding bridle, but with the addition of blinders and check rein.
Blinders restrict the horse's peripheral vision down to something akin to man's, and do not interfere with the horse's ability to see where he's going. They are widely used on driving horses to prevent the animal from catching glimpses of the vehicle he's pulling coming up behind him. The horse's instinctive reaction to such a stimuli would be either to spin around to face it, kick at it, or run away from it... None of which are acceptable actions when hitched to a wagon. Driving horses can be desensitized and worked without blinders, and some teamsters prefer it. But the majority of harness bridles have blinders built into them, so it's probably best for all harness horses to be accustomed to wearing them.
Check reins attach to the bit, pulley through loops in the upper part of the bridle, then attach to the harness. The standard check reins used on most draft horses simply prevent the animal from putting his head down very far, as having a horse in hitch trip over his nose trying to grab a mouthful of grass could result in quite a wreck. Such check reins are normally adjusted to allow the horse natural head carriage and movement... Fine harness show horses sometimes are subjected to top-check or bearing reins to hold the animals head in an unnatural position. These are of no use to a practical doomsteading teamster.
The equivalent to a riding horse's control reins are called "lines" on driving horses. Naturally, they are much longer. Lines are usually detached from the bridle when the horse is unhitched. Each line runs from the bit, through a ring in the hame (neck collar harness) or back band (breast collar harness) back to the driver. Team lines, designed for driving a pair of horses, are usually made in the form of and adjustable "Y" so that the driver only has to handle one line in each hand, although four separate lines can be employed.
Nylon lines are unpopular because they lack heft and feel. They flutter in the wind, and won't deliver a motivating
"slap" to a lagging horse's rump. Most drivers prefer leather or beta lines.