First, can you hunt successfully? When you are cold, exhausted, wet, desperate and hungry. hunting isn't easy or fun. Make sure you are practicing in all weather types.
Always have a good strong, sharp reliable knife. It is your #1 tool.
Bow saw is lighter, axe has a variety of more uses than wood blocking.
I would always bring a sleeping bag. In an emergency it will save your life.
Think about it. If the temp drops or for whatever reason you are stuck in the cold and can't form a better shelter then you are putting your life at risk. ALWAYS bring a sleeping bag.
The next thing you need to bring is a MED KIT.
You should never go hiking or wild camping anywhere without a med kit that you know how to use and opperate.
You also mention fire starters. FERO ROD! More reliable than a lighter and matches, though I would still bring lighter and matches.
Water proof everything.
At the very least take an extra pair of socks and jumper.
If I was you, spend as much time outside practicing.
Practice and pre pair, you will soon figure out what you may need and won't. MAP AND COMPASS.