Was the lighthouse a national park? If so carry is allowed in national parks and lake-shores.
As for the carriage, it's a gray area as the law only says vehicles, not motorized vehicles. The term vehicle is not defined in the statute and since it is not, the court uses the dictionary definition, which says a horse, bicycle, wheelbarrow, etc is a VEHICLE. Basically anything that transports goods or people is a vehicle in the broadest definition. So based on that, the statue is a gray area in regards to loaded weapons.