For a belt knife think very carefully about a Fallkniven F1. Developed for the Swedish Air Force. Those chaps know a thing or two about cold weather survival.

Ferrocenium rod.

Zippo lighter. You will have to keep it topped up, but it has certain advantages in a cold weather enviroment. Like it won't freeze up on you and is easy to use with gloves on.

I have used lithium batteries in my Petzle head torch. With no adverse effects. Only thing to remember is that lithium batteries give very little warning before they quite. Buy a head torch that allows you to put the battery pack inside your clothing.