In the TV series "The Tudors" 19th century carriages were shown conveying certain grand personages about on behalf of Henry VIII. WRONG. This was the point at which I began to shout at the screen. Coaches were not in use even by Royalty until his daughter Elizabeth I's reign, and they were uncomfortable, jolting unsprung things suspended on leather braces. Elizabeth complained of being badly bruised from being thrown about in a coach that had been driven too fast, and she was a fairly hardy lady. There was no glass in the windows at this time (guess why) and wheels were shod with iron rims.
Lots of authors forget that in a city, it was often convenient to travel in a sedan chair. Of course it didn't allow of company unless on foot, on horseback or in another sedan chair, but it had a lot of advantages over a horsedrawn carriage in the city. It was narrow and manoeuvrable so it could take you to places many carriages could not go, and the motive power understood speech! Also, in London and other cities based on a major river, watermen provided a taxi service up, down or across the water. John Taylor the "Water Poet" complained in "The World Runs On Wheels" that hackney carriages were taking away the ferrymen's business.
Steel springs made an appearance in the 1660s, and Sam Pepys remarked on them on a coach in London. He bought himself a private 4 seater carriage and two black horses, and probably employed a man to drive; and he seems to have been happy with his purchase, despite having to pay £2 to replace the glass in a window.
Commercial coaches were starting to appear on the roads. These were "stage" coaches which changed horses at inns along the road. One "stage" of its journey would be anything from 8 to 15 miles depending on the nature of the terrain. In winter, warmth for the passengers' feet was provided by filling the floor with straw - it works, but could be infested with livestock ranging from woodlice to fleas and even mice, depending on the diligence of the stable staff in providing clean straw.
By 1688, stage coaches ran from London to 88 different towns and by 1705 this increased to 180. However, Mail coaches were not seen until after the Post Office adopted John Palmer's suggestion to convey letters by coach instead of on horseback, following a successful experimental run from Bristol to London in 1784.
Smart light two wheeled vehicles for private use, such as gigs and dog carts, became popular from the 1800s onward. Four wheelers such as the various forms of phaeton were common. But for independence and access to open country, to make your own way to a destination, you rode - and were liked all the better for your active character, as opposed to being carried lazily about by carriage.
As for the curricle, that vehicle so beloved of the romance author, like a tandem of horses driven to a gig it was racy and showy and difficult and inherently unsafe... so beware which of your gentlemen you put at the reins. It was an owner-driven carriage. (I mean, you don't buy a Ferrari and let a chauffeur drive.) And don't forget that with a pair or team your whip, no matter how skilful, needs a groom behind him. Why? Common sense and safety... and the blasted curricle wouldn't balance without him.
Manpower and brakes
A gentleman driving his own carriage and four would have had one man, and more likely two, to see to tangles or mishaps with the horses. In Regency Buck, the hero tells off the heroine for driving his team with no groom to help her, because her passenger has an injured arm. Georgette Heyer knew her stuff.
Not even an exceptional "whip" - male or female - would ever have driven without a servant, because early coaches and carriages had no brakes. Down gentle inclines the horses could hold the carriage back with the harness, but on steeper ones the footman or guard got down and fitted an iron drag shoe under the gutter-side hind wheel. At the bottom of the hill, he got down again, the whip backed the team so the carriage wheel rolled off the shoe, and the guard picked it up by its chain and hung it on the hook again - not touching it, because it was hot from the friction! The guard or groom had to deal with broken harness, kicking horses and so on... or just to hold the horses when the driver and passengers got down at their destination.
Hand or foot operated brakes were late Victorian inventions which eased the work because the coach did not have to stop. They could still only slow the coach downhill; when loaded it weighed between 3 and 4 tons and the wooden brake shoes only operated on a 6 inch by 2 inch area of each wheel rim, so brakes couldn't stop it completely. Equally, rubber tyres for wheels were not invented till the 19th century, and they were solid, not pneumatic. Vehicles with rubber tyres tended not to have brake-blocks because they pulled the rubber off the wheels.
The idea of a "parking" brake didn't arrive until the advent of the internal combustion engine... a carriage you could turn off when you stopped. There are contemporary stories of coach teams being left unattended at inns, and taking fright or assuming a noise behind meant they were to start, galloping off with the coach with no driver at the reins... Horses require manpower, time and knowledge. Therefore - pretty please, authors - your characters driving a carriage can NOT abandon it at the roadside like a car, unless you want to plot a horrendous accident. You always need someone to take charge of the horses.
If you've got to describe a carriage drive or even a ride, it probably pays not to be too clever. Even simple things are very easily got wrong! For instance, you all know reins are for steering, and probably that traces come back from the horses' neck-collars to pull the carriage... the difference between the two purposes may seem obvious, but I've seen a mainstream published novel confuse the two.
Coachmen and good drivers held the reins in their left hand in an understated, workmanlike English coaching style and steered by turning the wrist, or by helping with their right hand which also carried the whip. They wouldn't drive with a rein (or two reins) in each hand; not unless you want to set them up to be ridiculed by their fellow drivers. For sheer style, watch any video of a British Royal parade with coachman driven carriages... the 2011 Royal wedding, or Trooping the Colour.
There is a big difference between sporty owner-driven carriages like phaetons (yes, and gigs and curricles), and sober coachman-driven carriages like barouches. It's very easy to get lost in their subtleties. For instance: pole chains. They were used to steer and stop commercial coaches, carriages and coachman driven vehicles, while pole straps denoted owner driven private vehicles... Probably best not to go into it too deeply unless you are prepared to read specialist books. Even the sainted Ms Heyer occasionally got things wrong.
Phew - I'd better leave waggons and farm carts and commercial trade carts for another day.
There, that got your attention, didn't it? I saved the best bits for the end.
Don't forget we have three genders in horses who are used as transport. There's the intact adult male, the stallion; the female, the mare; and the gelding, who is an equine eunuch and was probably "attended to" fairly brutally at the age of 18 months or so. Most working horses were geldings, whose lack of sexual interest made them easy to manage even for inexperienced staff.
Mares are the natural leaders in a herd situation - so they can be bossy. If they aren't in foal they come into "season" every three weeks from early spring to late summer, which means they may be distracted as well. Stallions have a sex-drive that rises and falls with time of year - up in early spring and throughout the summer, down again as autumn comes. To deal with either stallions or mares successfully takes tact and good horsemanship. So please don't have your heroine ride a stallion, unless you can also write about how she manages him in the company of strange mares, who will flirt by peeing at him if they're in season and try to kick his teeth in if they aren't. (Don't you love how horses can be upfront and obvious? My two favourite Fell ponies have been mares.)
In Black Beauty Anna Sewell tactfully fails to mention such matters, so generations of readers may well have assumed that Beauty's lack of sexual commentary simply meant that he had excellent manners, and that he was capable of retiring to stud and begetting. This is, sadly, very unlikely.
One final note
A horse in war, in a carriage, hunting or doing any other kind of work will NOT neigh or whinny when in a stressful situation - eg, battle or accident. You may hear a snort of fright, or a grunt of pain or effort, then the sound of hooves galloping rapidly away. Unlike movie heroines, horses do not scream.