Leigh,
I get cold feet from no reason. I can be sweating while my toes are getting numb. Go figure. Hands are the same.
I buy trail runners for the winter season that are at least a size to big. (Get anything at the end of the hiking season at half price. Fit doesn’t matter)
I start with a very thin liner sock commonly used in hardshell ski boots. I add a thin poly bag (tortillas, vegetables, etc.) I usually punch through it by the end of a day, and then throw it in the recycle bin. By slowing and containing foot perspiration you keep your insulating layer dry so it can do its job.
Then I add thick wool boot sock, then a NRS half millimeter neoprene “sock” – Hydroskin, $28 at REI. This will help keep the wool sock dry. Your feet will be damp at the end of the day, but not soaked.
Then the shoe and a gaiter, to keep the snow out of the cuff. The mesh on the trail runner gets filled, but no big deal.
It sounds bulky and awkward, but I do about 20+ miles a week in this setup in snow, and/or on snowshoes, and do just fine. Air temps 15° – 20°. Snow temps around 20°.
For colder days I go with a “Forty Below” Light Energy Overboot, with just a heavy wool sock.
YMMV