If your stove is installed correctly and properly cared for, then your small stove will not rust. If rust appears on the stove, it is usually because the stove has been exposed to moisture, possibly from the chimney. During winter, the air temperature of summer houses is often very cold, and the still air in the combustion chamber can cause condensation to form on the surface of the stove.
To combat this, you should leave the valves of the stove open. This will help to prevent condensation from forming on the stove, which can cause rust. Another good idea is to leave the door ajar when the stove is not is not in use for a period of time.