Battery management would be interesting on an extended climb. Battery Duration: 2.5 hours at high heat setting, 5 hours medium heat, 8 hours low heat. I would also be interested just how warm these gloves are when the battery dies. Sorry to hear about your frostbite. Hope you get a system that works for you.
I bought a pair of Serius heated mitts for dh area skiing last winter and found that I could get a 7+ hr day at medium heat without recharging. Problem that I found was little fingers would get cold because there is stupidly not a separate heated wire for that finger; perhaps I should have bought the heated gloves instead, assuming that each finger has a heated wire. I found chemical heat packs in OR mitts fine except for my thumbs, although hiking, xc skiing, and skinning usually provided enough heat to compensate. I paid over $400 for my heated mitts even after my SAR discount.
Edit: I misspelled Seirus above. The model is Innovation 3000 Ultra. A pair of 7.4 V 300 mAh 22.2 Wh Li-ion batteries tightly fit in the wrist pocket on each mitt or glove. At 125 grams (>1/4 pound) for each battery pair, the weight is not trivial on your wrist. I could see carpal tunnel syndrome happening with overuse.