>>2447334liner socks -> shell gloves -> overmittens
look at any mountaineering gear list for ideas of what works in extreme conditions.
shit that applies to working outdoors is not going to work as well for hiking, as its designed more for abrasion resistance and less for warmth and waterproofness.
you'll lose fingers trying to mountaineer in work gloves likewise you'll tear your fancy mountaineering mittens in 5 seconds trying to operate a chainsaw so pick appropriately to your trip's actual needs.
anon's advice to have your winter boots sized up for double socks is good. i typically wear a polypropylene sock with a thick wool sock over it in the winter, and when its wet/snowy a plastic bag between them as a membrane. sometimes even another wool sock over. yes this basically requires owning a dedicated pair of winter boots. avoid PU soles and its not an issue (pu will rot if not worn consistently)