IMO some of the cold feet syndrome is mental. People have a tendency to chase the warm, where warm enough is good enough. If you can wiggle your toes and feel it, you're not so cold to cause damage. A quick test is to press in your toenail until white and then see how fast the pink returns.
Wet socks are bad, it is simple, air insulates water/moisture is more solid and passes heat quicker. Two pair of wool socks, one over the other, works well for me, I've tried many dozens of the newest and best insulated socks and found nothing works better than plain old wool. Moderately insulated boots with two pair of wool socks and if you need it wrap your feet, boot and all, in another layer of insulation ( I carry a lightweight synthetic sleeping bag or sometimes a wool blanket with me for long high seat sits in cold weather).
If you get your feet too hot they are going to sweat, the sweat and soggy socks are going to steel warmth. I've found wick socks area a gimmick and have never helped me much, synthetics are moisture pass through and the inside of your boot gets soggy. "Wool's natural structure makes it incredibly effective as an insulator. Each wool fiber is composed of protein molecules (keratin) organized into five follicles. These fibers effectively trap air, moisture and harmful chemicals". Another tip is knee socks, have you ever noticed when you overheat while sleeping you usually first kick the blanket off your calves to vent heat, or wear shorts in hot weather. Keeping your calves covered with an extra layer of wool helps. The search for toasty feet IMO is a fools errand, your mind is going to trick you into never being warm enough and/or you are just going to sweat and the sweat is going to steel heat away from your skin. I've spent a lot of time in very cold to sub zero environments and have tried almost everything at one time or the other.
I've also never found anything better than German made Meindle boots. The inside of the boots are the key and their manufacturing techniques have been around since 1683.
A side note the reason your extremities get cold is your body automatically increases circulation to your core when it is seriously cold outside. In my experience, if you keep your, neck, your head and your core warm (especially your kidneys) your extremities are unlikely to get cold enough to stiffen.