It's pretty easy to put your hand with tab on in a pocket with a handwarmer pack.
For years I shot with a golf glove for this reason. Wool fingerless gloves over a golf glove works pretty well
Only the best glove for the job and the right amount of practice with it will tell you if it’s doable or not. I’m of the keep the hand in the pocket til the shot opportunity is imminent school of thought. Chances are if it’s so cold I can’t pull that off, it’s probably cold enough to hang in by the fire with my feet up