S.T.
Ah yes, chilblains! One of the more common problems I had to deal with as a podiatrist in the UK - it's cold and damp a lot over there, perfect for chilblains. Chilblains generally play up the most if your feet get cold, then you heat them up too quickly, so you need to try and keep your feet at a constant temperature. If you go out in the cold you need wool socks and insulated shoes, when you come in from the cold, don't stick your feet in front of the fire to warm them up quickly or use a foot spa, or soak your feet in bowls of warm water (don't know if you do that) but this consticting of the tiny blood vessels in your toes (or ears/nose etc), then rapid dilation as you warm them up too quickly. I don't know what connective tissue disease you have, but if you have scleroderma, then it is a very common problem because your skin and blood vessels are so unyielding and firm. There are various things you can paint on to try and ease them, but once they are there they are hard to get rid of - you need to try and stop them coming in the first place!
One remedy we used to recommend in the UK was friars balsam, paint it on, it helps a little.