Running cold water does not release humidity from the room in the same way that an air conditioner does. In fact, running cold water can potentially increase humidity in the immediate vicinity due to water evaporation. However, the impact on the overall humidity levels in the room will depend on various factors, such as the size of the room, the ventilation, and the duration of running water.
Air conditioners, on the other hand, are designed to remove humidity from the air as part of the cooling process. They cool the air by passing it over evaporator coils, which causes moisture in the air to condense and collect as water. This water is typically drained outside the home, effectively reducing the humidity levels indoors.
So, while running cold water may temporarily increase humidity in a localized area, air conditioners are generally more effective at reducing overall humidity levels throughout the entire room or house. If humidity control is a concern, using an air conditioner or a dehumidifier would be a more suitable option.