Apparently simple question: surely both. Simple it is not.
At first look, in the common situation, an open door in Winter is noticed because of the cold draft. We close the door to stop the cold air coming in. So yes cold is coming in.
The cost conscious might have a second level of worry that it is the loss of warmth, that they have paid money to heat the house. Heating up the outside world is a big waste of money . So they will see the heat escaping as the main thing.
Same situation both view points are true.
But surely only one thing is happening. Lets get atomic and do some physics to see what is going on.
Everything has some heat, which in physics is the physical energy of its atoms. Something warm has more physical energy than something colder.
So when a door is left open in Winter the air starts to mix bring air with less energy in and letting air with more energy out. So it appears that yes warm air inside is being replaced with cold air outside, and vice versa. Q.E.D.
Not so fast.
Suppose room temperature is 20oC all winter and then a day in Summer comes that is 20oC outside and we open the door. Would we ever say that warm air was coming in, and warm air is going out? 20oC was definitely warm air in the Winter and we firmly closed our door to keep it inside, but now there is warm air outside it doesn't matter and we open our door not noticing the air that is mixing.
In fact then 20oC is not actually "warm" air at all. It is only warm when outside is colder. Warmth is really relative.
So in fact there is more going on than just warm air leaving in Winter and being replaced with cold. While the air movements are purely physics what we are talking about and interested in is really the difference in temperature between the air coming in and that leaving. For this reason once we notice cold air coming in, we know for a fact that warm air is leaving. They are necessarily bound together. You can't have one without the other! To quote Newton: every action has an equal and opposite reaction. Now this looks like Dialectics at work!
So we see that subtly hidden in the opening of the door comes a situation of mutually reinforcing opposites. The colder it is outside the warmer it is inside and vice versa, and the more we want that door closed. Hot/Cold are inter-dependent. It is this inter-dependence of opposing forces in fact which ever stimulated someone to notice that the door is open in Winter while not in Summer. No one ever says close the door in Summer you are letting the air mix because the issue of hot vs cold is not being created. That event of "you are letting the heat out" is actually created by the contrast of cold and hot. Without the contrast there is nothing in the air itself that causes this.
Hot and Cold do not exist by themselves but always together in a pair. And when the contrast ceases so they too evaporate into nothing because at root they are nothing. There is no substance called cold or hot, there is nothing there other than them pushing against each other. This is perfect Yin-Yang in action.
So the answer is more than both, but necessarily both as if they were one... even while they are opposites. The whole situation is one thing, but composed from 2 ways of seeing it that depend on one another. And they are exactly dependent on one another so that without the cold there is no hot and vice versa. When the air outside warms up in Summer the whole hot/cold thing just disappears without a trace and the door just becomes a thing of privacy and security once more... which are themselves things caused just like hot/cold by dialectics.. as indeed if we look into it is everything!
A search for happiness in poverty. Happiness with personal loss, and a challenge to the wisdom of economic growth and environmental exploitation.
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