Yes !!!
Not so much on days after I get acclimated if it stays cold for a while. It's the changes in weather that I find are most difficult ... I call it my "AccuWeather Body"

I guess it's like any other "...itis" (inflammation) in the body, the NEURITIS of MS (where the myelin got chewed up) is affected by changes in Barometric Pressure. :-(
Like folks with Arthritis whose knees or shoulders ache, the weather can "get on our nerves" !

My legs get cold. I have to take a hot shower.

Yes I am so glad you asked that I thought I was going crazy. When it is damp and cold my legs are so stiff and hurt.

Yes!! The weather changes are a killer. Yesterday it was very windy, cold, and half snow, half rain. There wasn't one part of my body that didn't hurt. Today I am not much better. I feel like I can't get warm. Sometimes the only thing that makes it feel better is not to move. I have to find something quiet to do that doesn't require a lot of activity.

I have a lot of problems with the heat.....BUT.. the cold weather hurts, fingers hurt so bad drives my crazy. RX for this we need to move to a mild state-not real hot or real cold temps...start packing...Hope you feel better soon. Take care.