Again, what Ben said and practice with your glove on if you wear one.

I wear oven mitts over my shooting glove and bow hand. I can slide them off easily and quietly, and they are warm because of their insulating abilities.
I can also sniff them occasionally for the apple pie juice that spilled over...  

I really have a battle cold fingers here in Northern Mi in Dec, although this year Dec has been not to bad, AMs are really cold, I have been using ragg wool glove w fingers cut out, I have been putting the thin toe warmers with the adhesiveside on my palms! They are very thin and last about 3 hrs!I also modified a wool mitten w a slit on the palm that works well when it REALLY gets cold!The key is to practice shooting with what ever hand setup you use!

What Ben said , it works better than anything especially if you put 2 of the big hand warmers in there. I dont even have to were gloves with this system.

I've hunted in some really cold weather in ND and the best thing is the muffler like others have mentioned .If very cold you can use the chemical hand warmers inside and I use a thin glove for when it comes time to shoot . Mine has a small pocket on the front, I use it to carry my knife and a couple of other things. No disrespect but the glomitts were the coldest thing I ever wore .

A buckle-on hand muff and a heat pack.  I can't shoot in gloves.

Tim - I am gonna make me some of those one day! I remember seeing them in one of Paul's videos. I know just where to get the sheepskin for them.

I use army surplus wool gloves with fingerless rag wool gloves. I cut the fingers for my glove on the shooting hand. COuple of hand warmers in the pocket and i am good to go. Below zero weather, i will add a hand warmer to the back of my hand under the rag wool glove. Do they still make the wooly boogers? I remember seeing them a long time ago and liked the looks.

Insulated waterproof gloves for getting in to stand, thin merino wool gloves for on stand, and a muff with a chemical heat pack if it is super cold.

Chemical warmer pouch
Magnet not velcro for the mitten cover
Works with my tab

I hunt in Northern Wisconsin.
When it's below 30, I use a muff, and keep some hot hands packets in them as well.
I use a tab, and on my bow hand, wear a light glove. Been doing that since '95.
Works for me.

I usually wear some lightweight liner gloves that I can shoot with (I use a tab).
I can dry these easily, and often have an extra pair in my pack.

Sometimes, I also wear waterproofed insulated leather mittens over the gloves, as well as over my tab folded back onto my palm. I take the mitten off of my right (drawing) hand to shoot, and let it hang from a homemade leash.

I made a 6 foot cord mitten leash that goes inside my jacket and comes out each sleeve. This length is my wingspan.I used fishing snaps on each end of the cord, and tied some small loops on the cuffs of the mittens to snap into.

This way I can slip off the mittens and let them dangle, and they don't get lost or fall in the snow/water/mud. They are right there to put back on, so it is easy to take them on and off. I do not find them to be in the way for shooting.

The leash system is handy for me as sometimes I need the mittens on and sometimes need them off, depending on what I am doing, how hard the wind blows, etc. This way I don't have to take off my pack to stow or get out the mittens, so I can switch back and forth as needed.

Once rigged up, I can leave the mittens attached to the jacket by the leash going through the sleeves, ready for use on the next outing, and not liable to be forgotten.