Moss is not considered a decomposer. Moss is instead classified as a primary producer existing in the first level of the food chain.
Producers like moss, grass and cactus take the sunlight, carbon dioxide in the air and water from the environment and create energy (food) in the form of glucose (sugar). Moss grows in moist to wet areas and serves as an important source of food for herbivores in forests, where it's in what's known as the "litter layer," as well as in the arctic.
Decomposers are the final step on the food chain, rather than the first. Decomposers, such as mold, fungi and earthworms, eat the things that nothing else will. While a producer's purpose is to provide food, a decomposer's purpose is to clear away the matter that would otherwise bury the earth. In the process, decomposers refresh vital nutrients that producers need to grow.