I quite like neoprene gloves where you can velcro back the thumb and first 2 fingers. They are usually advertised as neoprene fishing gloves.
Handy when you need to maintain dexterity.
I'm a fan of these too - mine are made by Barbour. If it's very cold, I tend to wear mitts over the top, which are removed to shoot.I wear a pair of woollen knitted fingerless gloves when it gets cold in the winter.
Millar Mitts? They did work well in the late 80's which was the last time I saw them for sale. can't find any theses days.I should add that I also use Millar Mitts (cotton palm, woollen back and wrist) on the range in winter - but for hind-stalking and other wet activities, I find the cotton part rather chilly. Wet wool seems to insulate better than wet cotton.
I do this with gloves, but just cut across the trigger finger. Easy to bend your finger and get it out when needed.Try a pair of sheepskin mittens, cut across the palm of the trigger hand. When your hand is ‘balled’ they are the warmest thing you can wear, when you need more you can release all four fingers.