Desert rose will go dormant in winter and you can help that by bringing the plant under shelter to keep the rain out or bringing it indoors. The leaves drop but with minimal watering they will stay alive until they are taken out to the light in drier weather.
If it is outside and it is older then you have to be careful that it does not get too much water or it will rot. Young adeniums that haven't grown a "belly" yet can handle more water.
Sometimes spotting occurs when humidity is high and the plant cannot lose water by transpiration similar to what happens to geraniums when they get water too much in a condition called oedema. The water inside the plant cells have no where to escape so the cells burst and results in dead spots in the leaves.
Adeniums are native to desert and tropical and subtropical parts of Arabia and East and South Africa where winters are relatively dry.