That was drilled into us kids in scouts and hunters safety classes, plus instructions were in numerous books and magazines that boys read.
Snow caves will not ensure survival, especially if precautions are not taken. I well recall that a snow cave failed to save several people on Mt. Hood in 1986. One issue is that the clothing they wore was too light. A snow cave, if properly constructed, will not drop below 32 degrees for quite some time. This is because your exhaled breath provides warm air. The problem is you can still get hypothermia at 32 degrees if you are not wearing proper clothing. An ice cave is like being in a walk in freezer.