Lots of facts and numbers in this article, but safe to say that the weather contributes to levels of pain experienced by the respondents in this survey.
Almost half of the respondents claim 'heat' is the key to relieving pain ref. musculoskeletal disorders.
If your experiencing foot pain this study suggests that cold weather exacerbated pain.
If your living in a temperate climate and you not quite ready to move to sunnier and warmer climes then keeping in the warm would seem to make a lot of sense.
Whilst this sounds obvious, if your house has a few drafts then the area around your feet would tend towards cooler than the area around your waist, and or hands.
Sometimes you can feel warm but your feet are still experiencing the chill of these drafts... FYI
Mark