Hi. I have Raynauds phenomenon, in my hands one or two pairs of buffalo P&P mittens and a gtx over mitt as required. Feet my feet are okay in winter with two pairs of merino liner socks or Lorpen liners, leaving enough room to easily wiggle toes, I wouldn't recommend cotton socks, once wet they stay wet. I remember doing my winter ML in the late 90s and many participants had similar cold feet issues despite thick socks, but compression from lack of boot volume lead to poor foot circulation. Certainly something to consider.
I have dedicated winter boots for cooler, wetter, snow and ice, big clumpy boot warm and secure, as in a previous topic I use Trezeta Evo Top or Itturi cold weather high liability boots.
Now point two foot anti persperant, I never leave the house on a walk without spraying them, damp feet and boots conduct heat away from your feet, and also damp sweaty feet are more prone to blisters as wet skins tear and abrasion strength is diminished.