I was thinking today of the problem of dealing with emergencies in the woods while reading a post about hypothermia and an epic rain storm over 2-3 days.
I was also caught in a really difficult wind storm where the weather just became insanely windy and cold and was stuck on the other side of a pass for about 1-2 days. I didn't want to attempt the snowy pass with 40MPH winds.
In these situations it would be nice to be able to have a wood fire under your tarp. You can of course have a gas stove but this is extra weight and in an emergency situation you might run out of fuel.
I carry a wood stove so I have essentially infinite fuel.
I think the only problems would be:
1. venting exhaust / smoke / carbon monoxide
2. sparks hitting your tent and melting it.
However, within the confines of a good tarp, the rain shouldn't be a problem.
So one could jump out of the hammock and maintain the fire.
1L of hot tea can REALLY turn your spirits around.
If the hammock isn't full sealed the smoke won't be much of an issue other than maybe causing your gear to smell.
I think the biggest issue is sparks.
Perhaps one could carry a lightweight spark arrester in the form of a cheap metal mesh like those used in window screens.
The downside of course could be damaging your tarp but if you're not a complete idiot and keep the fire low and away from your tarp/hammock I think you would be fine.