While the main job of the breed was herding large livestock, they were also often used to pull small carts, carrying such things as milk to market.
So, why were dogs, such as Rotties, commonly used as draft animals instead of a horse, which could certainly handle a greater burden? There are several reasons. And most of those reasons lead straight back to the fact that a dog was the more economical choice under the circumstances.
For the most part, draft dogs were employed by small farmers. Perhaps it was a family with a handful of dairy cattle or a few chicken houses. Or perhaps they were subsistence farmers, who used most of their crops for themselves and could only spare a small amount to sell. Either way, in most cases, these were not big landowners. They did not have a huge amount of product to take to market and they did not have a lot of money to invest in a beast of burden. No matter what point in history we are talking about, it has always cost less to purchase a good dog than a good horse.
Let's look at the plight of a small dairy farmer. A horse would be using the same pasture as his cows, eating the same grass and grain. His choice might come down to the question of does he want a horse, or does he want to add another cow to his herd and increase the amount of milk his farm produces.
A dog, on the other hand, is not going to consume anywhere near the amount of food that a horse would. Also, the dog wouldn't be intruding on the cattle's food supply. While they are usually considered carnivores, dogs actually have some omnivore tendencies. The farmer could simply give them a serving of whatever his family was eating that evening. Plus, a dog could supplement its meals by hunting vermin or pests.
Also, in the case of Rottweilers, the dog could serve multiple purposes. He could be used to herd cattle from the pasture to the barn, in addition to pulling the milk to market. His protective nature made him an excellent farm guardian, as well.
In addition to those reasons why to use a dog, there were also health issues. As anyone who knows much about horses can tell you, the term "healthy as a horse" is a bit deceptive. Horses are actually very sensitive animals. Too much green grass in the spring and they can founder and go lame. A sudden change in the type or amount of grain and they can get colic, and possibly die. On the other hand, a farm dog would be much hardier (the term "sick as a dog" is also deceptive). And let's not forget the fact that you don't normally have to shoe a dog.
In the late 19th century, railroads nearly put the nail in the coffin of the drover dogs of southern Germany. It became illegal to drive cattle for long distances along roadways. However, Rottweilers still had their secondary occupation of draft dog available to them for several years afterward.
Unfortunately, though, they also soon lost that job as well. Donkeys became much more commonly used than dogs as beasts of burden. While a donkey eats the same food a horse would because if its size, it doesn't need near as much. In addition, they are much hardier than horses.
When compared to dogs, a donkey could pull more weight. It could also be ridden, something that even the biggest Rottie is not capable of. Like llamas, donkeys can make good livestock guardians, too, mercilessly chasing away anything that looks like a predator.
As with herding, the modern Rottweiler can still be used for carting. Only now, instead of an occupation, carting is now considered a fun hobby for both dog and owner.