In cold locations, it helps significantly to keep the rest of my body warm, and that in turn keeps my hands and feet warmer. I will actually over-heat my core to keep my hands warmer, because it gets really painful if I get cold. When my core is warmer, the blood flowing into my hands is warmer as well and heats them up.
Here are a few of the ways that I dress warmly for different environments:
This is a bit luxurious, but when I was preparing to travel to the frozen north to visit family in October, I knew that I needed to plan a way to keep warm. I started with a Columbia heavyweight baselayer shirt and pants. It has heat reflectors inside and is made of that awesome lightweight but oh-so-warm poly material. I also have a Columbia jacket that separates into two jackets or combines into one thick parka. This works great for layering and adjusting to seasonal changes on a trip.
I wear multiple layers with undershirts, dress shirt, and always an extra jacket. I really like the feel of knit tops with a jacket. I might wear two pairs of socks to keep my feet toasty and warm. I like thermal socks when I need a thin, professional-looking option, or a pair of thick 100% cotton socks if I can wear boots. (I also keep a space-heater under my desk, and that helps tremendously.)
We have tile floors throughout our home and it can get pretty cool in the winter. Consequently, a good pair of slippers is essential for comfort. The Baffin Cush slippers are pretty ugly, but they are miracles of warming science. The slippers are not a tripping hazard. They feel like pillows for my feet, unrestrictive, and as warm as a sleeping bag. With these slippers, I feel I can handle winter when it hits my home. The one downside I found with these is that when I washed them, they disintegrated.