Alternatively, keep some fingerless gloves around - or learn to knit/crochet/sew and make some (they aren't all that complicated for something basic). For around the house, you could honestly convert some socks if you aren't worried about how they might look. I'd get some of the no-fray glue they sell at craft stores if you go this route. These are great when you are idle.
Yes, doctor said I have poor circulation in my extremities. Except she said that using Latin, so that was super helpful. /s
From what I've read, the body primarily measures core temp around the chest, so wearing lots of layers on the body can cause the extremities to get cold since the body goes "everything is warm enough, no need to even try and warm things up with extra blood flow!"
So paradoxically, wearing less clothes can help.
What can the doctor do about it?
If anyone her wants to pay the postage from NZ, I'll happily send them around the world for no cost :)