There are two kinds of animal rights activists. The first see animals as people with fur, and the second are educated realists. My point is that there are economic considerations involved, especially with large animals that are classified as livestock. Many of the "animals as people" crowd choose to deny that.
Horses are used for labor, and the history hasn't been pretty. Heavy work and war have sent many horses to a premature death. Even in what humans consider high heat, pulling a light carriage on almost level streets is not heavy work for a 1,200-pound horse.
We often forget what the alternative to usefulness is for large animals. These horses are usually older, calm animals chosen for their docility. They may have been salvaged from slaughter because they are past any capability for hard work. It is likely that if they are retired they will return to the slaughterhouse. Green pastures would be nice for all retirees. But that's not realistic.
If you remove animals from public spaces, many people will no longer have the opportunity to understand why they are valuable. Some animals are partners in a joint effort. Horses deserve to be seen that way. They have earned it.