I also have issues with cold hands. I’m not a hunter, but our 3D season in SE Mass starts the first week in January and we’ll have a few really cold shoots each year. I use a combination of what’s already been said here.
For my bow hand, I use a glove liner under an insulated leather work glove with a chemical hand warmer between the two. For my string hand I use the around the waist pouch (just like Tom Brady!) with several chemical hand warmers stuffed inside. For me, the most important thing is to buy large amounts of cheep hand warmers so that I’m not tempted to skimp when I’m reaching for them before going out. I’ll use at least 3 down into the mid 20s and 4 or even 5 as it gets colder. It would be too much heat if I kept my hand in there all the time, but I keep it comfortable by going back and forth into the pouch. It makes a big difference to be able to really heat up your string hand right before a shot.