my feet get cold, but I live in Alaska where our inside temp is 67f degrees and most of the time I forget my slippers. They will get cold also if my circulation gets compromised. I do have a tendency to get cold hands as well. The past several years I have had issues of getting cold in general. I use to be able to tolerate cold to some extent (being in Alaska), however now if I even get a slight chill, I will shiver and my muscles will tighten to the point that I cannot move and on one occasion, I passed out from pain and my throat muscles clinching and cutting off circulation to my brain. Thus, I will never get in a cold car again.
So whether this answers your first question or not, that is my experience.
As for other treatments, do what is helpful for you to feel as relaxed as possible. As you said, they will not change things in the long run, but if they give you temporary relief without you needing to take medications and you can afford them, the all the best!
I use to find massages very relieving for me years ago. But there was only one masseuse that could do it right and turn me into a bowl full of jelly. He would use some ointment that would remove all the pain and he knew just the right amount of pressure to get a muscle that would be knotted to release. He has retired (and since passed away), and I have yet to find a replacement who used whatever technique he used. My husband can do some good, but he looses interest or gets tired. He is not a professional at it. Other masseuses I have tried usually end up making me feel tighter because they try to rush through and either barely touch me or kill me from doing it too hard. So I have given up on finding one. Got too expensive since no insurance would pay for it.
As for yoga, just be careful of not falling over from some of the positions. I have been unable to fix my balance at all. Mainly because as my muscles weakened over the years (very slowly) I would discover that one day I could do something, then the next day I would fall over doing the same movement and never gain it back. Or I would rip a tendon putting stress on a muscle that had seemed to get weak without me noticing. I use to do the Wii fit program with my daughter quite a few years back. Did all the yoga and loved the ski jump game. Then one day fell into the tv set because I suddenly discovered I could no longer lean forward with knees slightly bent and be up on the front portion of my feet, like you would when skiing. Had done it with some pain just the day before. Never could do it since. Of coarse now I cannot walk farther than a few yards at a time, so keep moving and doing what makes you comfortable in order to keep moving! Just be careful!