When people add coaches, carriages, wagons, and carts to their stories, they often do enough research to find out they may have something called “brakes” and then treat them largely as autos or trucks with horses up front. (Less often, mules, donkeys, camels, zebras, oxen, elephants, or carabao, not to mention moose, caribou, goats, or dogs for motive power.)
In an auto, you can be zooming at freeway speeds, stomp the brakes, and come down to a complete stop. But auto brakes are complicated and highly engineered, even before they were computerized. You have the force multiplier of hydraulic systems in power brakes. You have the brake shoes exerting friction against the whole brake drum.
On a carriage, you have a pivoted stick exerting friction against several inches of the iron tire on a four-foot-high wheel. That’s all.
Let’s get the variations that make no difference brushed aside and call it a horse-drawn coach. Think of it as a British mail coach or a frontier stage coach or a polished private coach – doesn’t matter. What matters is that none of these can be stopped at any notable speed by the mechanical brake.