You may use an outhouse or outdoor bathroom in all kinds of weather. A roof protects you from snow, rain or hail coming in while using the facilities and also keeps the interior clean of sticks, leaves and other natural items that may blow in during windstorms. Without a roof, an outdoor bathroom would wear out much faster from water damage and would become dirtier inside much more readily.
In northern climates, an outdoor bathroom can be a chilly place during a good part of the year. A roof helps to create a closed environment inside, keeping wind outside and any residual body heat inside. Having a roof can mean a tiny difference in indoor temperature in an outhouse, but that small difference can be felt during the worst weather.
Outdoor bathrooms are almost invariably placed in out-of-the-way spots close to nature. Whether in a park or in back of an old farm, small climbing animals would drop into an outhouse without the inclusion of a roof. Although these creatures may still invade the interior through the door or under the edges of walls, having a roof will lessen the chance of a full-scale infestation.
Many people have been raised with strong privacy feelings toward bathroom habits. They always close doors when using the facilities, even outdoors in nature. Having a roof adds a small extra feeling of privacy that an outhouse would never have if the top were open to the sky, which makes the users feel more comfortable when needing to use the facilities.