Can you travel by Horse and carriage to a quest location ? The location could be in a hard to reach place.

Horses have been known to run up a mountain, but Carriages do not leave Main Roadways. A Horse can take a character to places the player could probably never reach, but Carriages in Skyrim are limited to Hold Capitols.

One quest requires horse and carriage to location.

Other than that, those carriages only go to specific places ( hold cities/towns stables).

The carriage system allows the player to unlock cities for fast travel and then you can explore the areas nearby to discover locations.