I'd go with full rain gear - jacket, pants, shoe covers, helmet covers, hood for in camp (I don't like to ride with a hood under my helmet - I prefer a helmet cover), and waterproof winter gloves.
I think a hatchet is pretty worthless. When car camping I only use mine for splitting kindling.
My tool kit:
- a Swiss army knife,
- a multitool with a hex wrench big enough for my crankbolts and a chain tool,
- a hypercracker cassette removing tool,
- a spoke wrench if the multitool doesn't have one,
- tire irons,
- a patch kit,
- at least one extra tube.
- I carry two extra spokes and one of those kevlar emergency spokes.
- If I'm going to be far away from bike shops for a lot of days I'd carry two tubes, and maybe a spare tire, although I usually just tour on new or almost new tires and have never had a tire issue.
- I bring some Loctite and a few zipties.
- I bring a couple of spare bolts to fit my racks.