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.