You can throw them in a fire to burn out any residues, but afterwards you should pull them out, smash them and pack them out with the rest of your garbage. First, make sure you do so in a safe location. This is doubly and triply important during the fire season. Many, many fires have been started by careless smoking and improperly disposing cigarette butts. Secondly, when finished putting out the cigarette, place the butt in a baggie and carry it out.
Orange peels are organic, but they are one organic that lasts a long time.
Even in wet climates, orange peels can last for weeks. In some very dry climates they can last for years. They are unsightly and should always be carried out. Peanut and eggs shells. If you have a fire, they can be burned, but watch egg shells since often they don't burn completely.