I have a pair of mid-tier and I didn’t think they were worth the money. I think the chemical handwarmers are better.
However, my wife has a pair from a company called Ravean that she really likes. Of course, the coldest weather she would ever intentionally experience is spring skiing so I can’t say they’d work on top of a real mountain.
This is not a mountaineering recommendation but the warmest gloves I have (warmer than the arc’teryx SV mittens) are from a company called Atlas that makes industrial safety products. I’ve used them in single digit 100% humidity howling wind weather for getting duck decoys out of the water and been toasty warm. Cost about $25/pair. Made from bright orange vinyl and are completely 100% waterproof. They are like wearing boxing gloves though so I doubt they’d work on a mountain.