Yes, good advice! Our PNW weather can go down to -10C/14 F up to 10C/50 F, but usually hovers in the 5 C/40 F range, but very damp, chilly cold. So we aren’t as extreme as some places, but have the added problem of staying dry.
On the other hand, I get cold faster than a lot of people, apparently, so my advice on dressing for weather might apply to colder places too! 
What everyone has said about head, fingers, toes and torso: yes.
I like merino wool as a base layer; I wear wool long underwear under my fleece Kerrits full-seat winter breeches. And a wool undershirt really warms you up. Or a microfleece long-sleeve top as an undershirt. Then I have a lighter-weight wool pullover, and then a zip-up hoodie that is poly fleece on the inside, smooth finish on the outside (double sided fleece picks up too much hay!).
Then the outer layers Down is great. I have a lightweight down jacket that they call a “down sweater,” a down vest, a Goretex-type rainshell, which can all go together as one “outfit.” And then I have a heavy-weight Goretex-type down parka.
If I’m doing a serious lesson, I can strip down to the hoodie layer. But always have the parka layer at hand, because you do cool down fast.
Wool socks. Insulated boots. I wear insulated paddocks boots and half-chaps when it’s cold.
And you can get those little one-time-use heating packs and pop them in your gloves, on top of your hands. You don’t even notice they are there, but they make a huge different.
And fleece gloves. I was buying equestrian gloves for a while, but they tended to fall apart. I’m now using North Face “glove liners” that are smooth outside, fleece inside, and have silicon grips on the palms. Some of the other sports companies make similar.
Cotton is not your friend in the cold. I do sometimes get into my cotton-knit breeches, when it is up around 40 F, but only with merino long underwear.
