I use a pair of fingerless gloves - very snug fitting, made by Black Diamond. Over these go a pair of large mittens, with a single finger, insulated with Thinsulate and waterproof. The mittens have wrist hang ties, so that I can take them off, they then dangle from my wrists, and I have some protection from the fingerless gloves to shoot.
After shooting, hands go into pockets with chemical handwarmers, then back into mittens. You could size the mittens to allow for chemical hand warmers.
Hope that helps. I have a buddy with Raynaud's, and he uses the chemical handwarmers from fall through spring.