The statement "you're letting the cold in" is technically false. When you open a door on a cold winter night, you are allowing the warm air inside to escape, which can cause a drop in temperature. However, you are not necessarily "letting the cold in." The cold air is already present outside, and it will continue to exist whether the door is open or closed. In fact, the temperature inside your home may only change slightly, and it will depend on many factors such as the size of the room, the amount of insulation, and the efficiency of the heating system.
The concept of heat transfer, which is the movement of heat from one place to another, helps explain why this statement is false. When you open the door, the warm air inside will move to the cold air outside, which is known as conduction. This transfer of heat will cause the temperature inside to drop until the heat source can warm up the air again. This process will continue as long as the door remains open. So, while opening the door on a cold winter night can cause a drop in temperature, it is not because you are "letting the cold in." Instead, it is because you are allowing the warm air inside to escape.