This is really non-intuitive, but the best pair of gloves you can buy is a cold weather vest and a thick stocking cap. Down is great, but I sweat so one of the new fancy fiber filled works best for me. Right after that, good underwear, or more convenient, zip on insulated ski pants. Layers, so you can unzip a bit at a time to keep from sweating. It's all about your core temperature. Head, torso, armpits, groin are big radiators. Can't remember which order they're in, but hat and vest come to mind as 1st and 2nd,,, but just try it,,, you'll be amazed at how cold you can work bare handed in. Oh,,, and the bonus, warm and toasty toes;-)
Best place for the hand warmer? Not in the gloves,,, put it in a chest high vest pocket. I really like the ones that use the charcoal sticks,,, Dad always used the fluid ones.
Sailor supply store, (or if you can find some military surplus) have long, cut off finger wool gloves. Get huge mittens to wear as over shells until you need your fingers. The old military wool liners and mitten shell were great. The liners had an opening like your pants fly in the palm so you could get your fingers out as needed. Three fingered. And the outer liners had fur on the back of the hands for your nose. (quit laughing, it's important to be able to wipe your nose without exposing your hands).
One more,,, at the ski shop/ mountain supply place, get some silk hand panties (ok,,, my description) the silk gloves under everything. Very thin, but offer that last little bit of protection, plus they wick sweat away from your skin. When the winds howling, the temps down, it's almost the same as a bare hand, but protects just a little against frozen metal parts.
Here's the trick. Slightly overheat your body, which will then use your extremities to cool itself. We learned that in the 60's during cold weather training in Ski Patrol, there was even something on the Discovery(?) channel about a military study not long ago that really confirmed it.