What are some common causes of bone pain in cold weather that is not related to arthritis?

Not sure: That's a tough one. I am not really sure. If you are having pain only when it is cold and not when it is warmer, it is probably arthritic but as to other causes, there is a condition that I have never seen but we learned about in med school called cold cryoglobulinemia which is an inherited condition in which proteins in your blood become thicker in the cold and can cause pain. Unusual though.

Soft tissues: I call this the barometer sign. Change in weather symptoms can occur with the increase in the humdity and drop of barometric pressure. This may cause pain in the joints, in the bursas, in the tendons. Most of this pain you inquire about is in these soft tissues.

Inactivity: Muscle stiffness is the most common cause. If your bone pain is localized and pressing the area/areas is tender, definitely inflammation is the cause.

Raynaud's: is a disease in which pain can occur during cold weather or winter. Although not typically associated with bone pain it does cause the local bold supply to thin out result pain due to the lack of that blood supply.