I am inflicted to some degree with peripheral and autonomic neuropathies, and it does sound more like some kind of muscle strain or tendonitis; but, I am no medical expert, so I will go with the others and recommend a swift visit to your GP.
Don't forget that when we get cold, our circulation cuts down to our extremities in favour of our essential organs, and of course, your feet will suffer all sorts of weird feelings as the circulation slows right down.
Just as a matter of interest. . . google raynaud's syndrome and see if that could describe your feet.