This sounds a lot like the symptoms of Raynaud's disease (aka Raynaud's phenomenon). https://www.mayoclinic.org/diseases-conditions/raynauds-disease/symptoms-causes/syc-20363571
It's not life-threatening, but it certainly can be uncomfortable. I recently moved to the southern US, but used to live in the midwest, and I am pretty sure I had a mild case of Raynaud's. Unless it was really hot outside, my fingers were always cold. Winter was pretty awful and I felt like I could never get my hands or feet warm if I had to go outside, even after being back inside for awhile.
Soaking your hands/feet can help, but don't use water that's overly hot. It will hurt like crazy. Just use mildly warm water, and then increase the temp after you get used to it.
My wife has RD and she manages it well it by doing the following :
1. Cold avoidance
2. Increase Nitric Oxide (this is HUGE!!!)
Nitric Oxide (NO) is a signaling molecule produced by the body, and is a vasodilator that helps control blood flow to every part of the body and a lot more!
3. Reduce stress
Please look also into a study titled : "Helicobacter pylori eradication ameliorates primary Raynaud's phenomenon"
If you need any more details, just let me know.
I have not only studied NO, I implement NO boosting strategies in my everyday life
to prevent HBP, high cholesterol, Erectile Dysfunction, Reynaud's, strokes, heart disease, etc. without the use of any drugs!
I have to mention that my comments are not intended as a substitute for medical advice.