I love horses. I've owned a handful over the years. This photo is not one of mine. He's Samson and he belongs to the Amish neighbor who cuts and bales my hayfield. He's a real working horse, just like those we write about.
Here are some horse scene disasters I've read in books recently. I'm paraphrasing:
She took off his bridle and slipped his harness over his head.
The author meant to use the word "halter" and not "harness." A harness is what Samson is wearing. It's a series of leather straps and metal buckles that attach the horse to whatever he's pulling. When tying up a horse, one uses a halter, which fits only over the horse's head.
She shook the reins and they rode off.
When riding a horse, you don't shake the reins. Riding reins are connected to a bit with a shank, a metal piece that extends down from the bit. The shank makes the bit's pressure more exact on the horse's mouth so he can understand the rider's commands. Shaking it would confuse the animal, giving it mixed signals. A rider touches the horse's sides with her heels to move the horse forward. The reins and bit are used only for direction and stopping the animal.
The horse loped along pulling the buggy.
Horses don't lope, canter, or gallop when pulling a buggy. Buggy horses are either trotters or pacers. Here's a good youtube video explaining the difference. While a horse can pull at a faster gait, it's not desired unless being chased by Indians or bandits, and even then it's extremely dangerous. At a lope, canter, or gallop, there is a point where all four of the horse's hooves are off the ground. If at that point the buggy were to strike an obstacle or fall into a rut, there is nothing to stabilize the buggy and a disaster could result.
What about the stage coaches? Yes, they were sometimes pulled at a faster pace, but they generally had four or six-horse hitch, so they were stabilized by more than one horse. Even so, the romantic notion (or Hollywood portrayal) of the galloping stage coach is mostly that - a romantic notion. A horse can go longer and cover more ground at a trot than at the faster gait.