I've always been a fan of mittens or the "lobster mitts" that allow a bit more dexterity. Keeping the fingers bunched together keeps the hands warmer. I think it depends on how much dexterity you wish to keep though. I find hiking in the winter that mittens are fine. XC skiing though I usually opt for gloves.
Not sure if you need the battery operated setup. Might be a bit overfill.
Like others have posted too. Good circulation is key!