You are right about heat and snow. And the fire too close could cause melt. It depends on the cold. If very cold, and a clear night can give that, a little fire with a foil reflector can help keep the head warm. But then, so does a good wool cap, tuque, or fur hat etc. You can wrap yourself in a tarp to keep the wet snow from soaking your sleeping bag etc.
The green wood is just small branches cut from a living tree. Being green or ‘wet’ it is less likely to burn up in the first hours. It is also easier to bend into shape, and to cut. Dead wood is very hard and using a knife on it can lead to nasty accidents. The green wood is used to make a frame for the aluminum foil reflector. It can be used to meke frames for a tent.
A good knife has good steel; that means it can be sharpened and stays sharp a long time. Some of the older knives are very good for that. Newer ones can have too much molybdenum, and this can make them too hard, and they won’t sharpen unless you use a grinding wheel, then a file set, then the wet stones.
I once saw my father go into the bush and cut a two inch diameter sapling, it was poplar, in a couple of minutes with his four inch blade pocket knife. Just sliced into it like it was butter.
Bonne nuit, belle etiole