Bag Balm is for fixing what's already broken, and will work well for reviving traumatized skin. I recommend you spend some money on gloves+mitts so that your fingers never get that messed up.
Latex gloves are an interesting idea that I'd never thought of, and worth trying. For ultimate dexterity there are fingerless liner gloves that work amazingly well. As long as they are VERY long in the wrist they will keep your hands and even your exposed fingers warm enough.
I use thin semi-liner gloves that are a little bit like gardening gloves. Like the cotton gloves previously recommended, only they are POLY and they have grip surfaces on the plams and fingers. Poly will not soak up water like cotton.
Either way, you also need snowboarder's mitts. These are warm and HUGE like eskimo mitts, so that they're easy to slip on and off over your thin gloves. You will not be able to grip anything with them, but even a few seconds inside them and your hands will warm back up. For really miserable tasks I will expose my hands in shifts.
