Have you considered wrist warmers? I have seen them marketed out there online, but basically a pair of sweatbands covering the wrist warms the blood as it enter your hand thus, circulating that warmth. Have passed this on to a few others over the years either RNLI crew or outdoor enthusiasts and it works.
When out on the hill, especially winter, I normally wear a thin pair of gloves that are great for manual dexterity work like navigation, compass bearings, etc and have a waterproof pair of either mittens or mountaineering gloves over the top depending on what I'm doing - mitts for general walking and gloves for technical work, i.e, using axes or rope work.
Always carry spare gloves when youre out CG, you will ALWAYS have wet gloves regardless of activity and if the wind takes a pair out of your hands, you always have a back up pair in your sack - think redundancy.
Give the wrist warmers a try first and adapt hand layering depending on the task or the warmth needed. You could make your own by using cut offs of neoprene from a wetsuit, utilise the ends of a support bandage, etc. If you find it makes a difference then go ahead and invest in a pair that work for you and your activity.
Stay warm!!
Any suggestions?