The following is what I gleened from the story:

1. The unexpected can can happen at any time.

This is evidenced by the simple act of going into a forest to collect a Christmas tree and getting lost.

2. The mind is the best survival tool you can have.

The Dad only had the clothes on his back and a saw. Yet, he built a crude shelter the first night and built a distress signal from available materials that eventually lead to their rescue. Recognized health hazards and developed a way to treat them with what he had.

3. Attitude is everything.

Kept his kids alert and interactive with his positive attitude despite the gravity of the situation.

I could play the "shouda-woulda-coulda" game and try to second guess their precise situation but the bottom line is they survived with minimal injuries from a potential deadly situation. For that, they should be commended.
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“Always remember the 6 P’s”
(Prior Preparation Prevents [censored] Poor Performance)