Let me go over the obvious.

Hypothermia may be the number one killer in the outdoors. If so, then, after breathing, staying warm, or if you need to getting warm, is the priority.

In cooling wind, rain, snow, etcetera, you must get out of the elements to preserve body heat - you need shelter. If a good insulating shelter is found or created timely, then your own body heat can sustain you for quite a while. You will then be able to survive without a fire for a time, so long as your body fat or uncooked calories are available to keep your inner fire stoked.

If you have lost a lot of body heat and / or you cannot find or create a good insulating shelter, then you pretty much need a heat source to survive, be it a fire or a willing friend or two. Once body heat is restored, see above.

You can die in 3: minutes without air, hours without shelter in a cooling environment, days without water, and weeks without food.

Any way you slice it fire is important. I do not think the debate on whether shelter or fire is more important can be answered out of a specific context, but this thread is intended to focus on two fire-related topics: keeping it going and taking it with you.

Let the games continue!

Edit: Please forgive exclusion of desert-type dehydration hazard environments.