The accident reportedly happened on a road leading from the car park to the castle at around 12:30pm on Monday.
Eyewitnesses said the two horses of a coach carrying seven tourists bolted downhill away from the castle. The driver apparently leapt from the vehicle as it began moving, suffering minor injuries.
A mother and two children, aged nine and eleven, were thrown from the carriage when it hit a wall after around 500 metres, local radio broadcaster Allgäuhit reported.
The carriage then continued down the hill where it rammed into a parked coach - containing no passengers - and a tree. The driver of the empty coach was knocked off his seat and fell to the ground.
The first coach then continued some distance before getting stuck on a tree trunk, where the four remaining Japanese tourists on board were thrown. They suffered minor injuries, but the two horses had to be put down because of the severity of their injuries. It remains unclear why they suddenly bolted.
Several ambulances were called to the scene. The woman and two children who were thrown first are said to have suffered serious injuries and were taken to hospital by helicopter - the other six people involved are thought to have escaped with relatively light injuries.