Why do my feet sweat in the winter when I'm relaxed (not stressing), insufficiently warm (cold all over), and not sick?

Feet can. sweat for many reasons….sometimes because your sweat glands are overactive which can occur no matter what season your in.
Autonomic regulation. Possibly related to some autonomic regulation problems, when you body has troubles tolerating change in temperature. It is inconvenient, but not dangerous, unless you have other signs of heat- cold intolerance ( potentially could be a sign of thyroid problem)