As a lifelong mountaineer interested in alpine and scottish winter ice climbing I have a little experience of weather sufficient to freeze the barnacles off a brass dinghy (or words to that effect!). I wear silk gloves underneath DACHSTEIN woolen mittens. The Dachsteins are amazingly thickly woven and like toast.
For my stalking I substitute thin leather shooting gloves under the mitts and then it is simple to slip off a mitt to take the shot, keeping the leather glove on.
If like me you are prone to mislaying things in the excitement of the kill just do what your mum did with your gloves when you were little - tie them together with a length of string threaded through your smock sleeves. Whilst your mates might mock, at least your hands will be warm.