My current mitts are hand knit mitts of a coarse felt resistant shetland type wool, like Briggs & Little, which is a very warm when wet and very resistant to fleecing. They don't stay wet, unless its continuously raining. You can shake them dry. The wind blows through them to keep them dry and your hands comfortable in all conditions so you don't have to keep taking them off. I will be make a pair of scrap nylon overmitts like phat. Extra long elastic wind or rain shell sleeves can also work as overmitts. If you can get a pair of thin single knit wool gloves that fit your fingers just right, and tighten some when you try and pull them off, these can be very good to wear in cold rain and still be able to tie shoelaces or tent cord or even a hatchet, and stuff like that. Again they should be a strong wool that is resistant to fleecing. They can be surprisingly warm when wet even though they are thin. These could be carried with the hand knit mitts, and together with the nylon shell you would have something for sustained periods of very cold weather. You want to avoid wool mitts and gloves that felt to easily, as they will not be so good once wet. Stuff like alpaca and angora and rag wool is not so good once wet. However, Alpaca is excellent for hats and neck tubes. I don't think mitts and gloves should be double knit or thrumbed. Better to have thin wool gloves, and separate wool mitts of a thicker wool, but single knit.

Hands don't need as much insulation much of the time, but they need just as much for sustained periods of extreme cold, and perhaps a little more to get warmed back up again after getting exposed and wet to get something done. Wearing socks as mitts can be a good way to dry them out, or to give you an extra layer when its really cold and your just resting or trudging along, or if you need to get them warmed back up and refilled with blood.