As someone who doesnt stay ENTIRELY in the woods, but often spends a large amount of time there:
Survival, fabrication, tailoring, construction (if setting up a proper base) are all pretty useful skills.
Cold is beaten by getting some form of tent, if refusing to use buildings. A tent and good clothes can keep you warm through all but the coldest nights. You can make various makeshift tents/shelters using survival, I believe. It may also be worth going underground into a cave - they tend to have less variable temperatures.
Campfire drill served me well for a long time. There might be something better, but a drill is sufficient.
Foraging in the bushes can sustain you for a time, but if you need more food than that, good sources are: Ant hills (ALL the meat), swamps if you can take on swamp monsters (again, lots of meat and you can harvest cattails for both food and fiber), growing your own if you have the time and patience. I’ve heard good things about fishing, too, but there were no rivers near me when I did the wilderness stuff.
Easiest way to preserve food is salt. You can easily acquire this from salt water tiles in swamps, though be careful of monsters. You can also set up a smoking rack if you are dedicated enough, and smoked meat keeps just as well as salted. If you can put together a chemistry set (not sure if this is possible if staying entirely innawoods, but if you are still allowing labs and such it is easy) you can make sugar from fruit and then preserve other fruit as fruit leather. Acorn meal never goes off, same with flour you make from cattails/acorn meal.
tbh I mainly cheat the nutrition syste with multivitamins. I can’t help you here.
If looking at weapons, you should be able to get some spears together from nearly nothing without too many issues. Those will at least help taking most enemies down early - reach is a powerful thing. I’ll be honest, I punch my foes to death, so I cant help much here. Putting together a bow, or a sling if really early, seems like a good idea though.
