10

From this answer, -148 °F has been survived inside a snow cave, and this question is asking for the unadjusted temperature, which leads me to wonder how much the wind chill would matter.

If you have your cave built properly, you should be out of the wind, except for the holes necessary for ventilation (some air will get through snow, but after time an ice layer will form inside the cave and need to be scraped away).

How much does the wind chill matter if you are inside a snow cave?

21

The concept of wind chill does not apply in this situation. Wind chill talks about perceived temperature due to additional heat loss due to convection. Meaning without wind, the "heated" air will stay around you much longer, thus "insulating" you a bit, while in high wind any heated air will get swept away immediately.

In a properly built snow cave you have no wind. Sure there will be some air exchange through entrance/breathing holes, but diffusive. Air holes mustn't be big enough for wind to get through and the entrance should be built wind proof (position, snow walls, stuffing your pack into it, ...). This air exchange is relevant to the temperature difference you reach to the outside, but it is not wind chill.

3

None,

which is why having one is nice for survival. Wind chill comes from wind over exposed skin, unless your snow cave is badly built - there will be no wind.

Do note that wind chill is also a non applicable factor if you are not exposing skin. Wind chill is calculated / modeled directly from tests with humans and exposed skin - the value literally does not apply to non-exposed skin. Wikipedia among others, state that "[Wind chill] is determined by iterating a model of skin temperature under various wind speeds and temperatures using standard engineering correlations of wind speed and heat transfer rate." Wearing protective layers that shields you from wind makes the assumptions behind the wind chill calculations very off the mark. Now, without a doubt and for absolute certain, you will feel colder and you will get frost bit sooner but the concept of a wind chill temperature only applies to bare skin.

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