Try this for a week and I guarantee it will be better.I've been dealing with arthritis, especially in my main thumb joint on both hands.
Also, have been getting cold hands. I simply work the thumbs through the painful stretches and bends to get them loose and more flexible.
I'm not concerned with cold hands. They warm up quite quickly.
Just for reference purposes I just turned 77.
For me, it kept getting worse. The bathroom sink worked for a while, but took longer and longer.I've also been experiencing colder hands and stiffer joints as I'm headed into my mid 60s. I find the hot water in the bathroom sink before hitting the stage works spectacularly. A good bit of hot water, for 2 to 3 minutes, and it feels like I've been warming up for an hour. I'm assuming my condition isn't severe as yours, but yes, I have a marked difference versus when I was younger.
This method, just for 2 minutes per hand per day, seems to eliminate the need for bathroom sink alltogether, and actually improve circulation. Where as the hot water will actually let your blood vessels "know" that they dont need to open, cus the warmth comes from outside. IME it actually sped up the decline.
That being said, I live in a cold climate.