Yes, dark brown cast stone can be used in exterior applications in very humid climates. Cast stone is a highly durable and weather-resistant material that is commonly used in construction. It is made by mixing crushed natural stone with cement, water, and color pigments, and then casting it into specific shapes.

The color of the cast stone, including dark brown, is typically achieved by adding iron oxide pigments during the manufacturing process. These pigments are resistant to fading and can withstand exposure to harsh weather conditions, including humidity.

However, it is important to note that the overall performance of the cast stone in a humid climate will also depend on other factors such as the quality of the manufacturing process, proper installation techniques, and maintenance. It is recommended to consult with experts or manufacturers who can provide specific guidelines and recommendations for your particular project and location.