Well, i actually agree that the head and neck is about %25 of your POTENTIAL heat loss or gain due to the amount of blood that flows close to the surface. Your blood is liquid cooling/heating along with nutrients like oxygen for they organs. No matter how bundled you are if you go out in the cold without a hat you're going to get cold.

I've got a backpack for a real BOB and the car kit is just an old shoulder bag i found somewhere. You could use a soft sided lunch bag, or just roll it up in a tarp or blanket and tie off the ends. I tend to keep stuff shoved in with the spare unless it's mounted under the vehicle so I'm not tempted to put it in the house "just temporarily".

Having water in the kit itself is troublesome due to colorado weather. Alberstons use to sell a bag o water that was about 20oz for a buck that didn't leak when frozen even multiple times. don't know if they still do, even stale water is drinkable. consider coolaid singles or the like to cover the taste and add some electrolytes. It also sweats so keep that in mind when you store it in your kit.