I live in eastern Canada and ride outside all winter in -15C temps. I try not to ride in -20C but with the wind, it happens. Even on a milder day, it doesn't take much wind (remember, you'll be creating your own as your horse moves) to make the temperature a LOT colder!
First, you need a helmet cover. Really, to me that is one if the necessities, and they're not that expensive. They cover your helmet and have a fleece flap with velcro that covers your lower face. This will save your cheeks. On milder days, you can wrap the velcro around the back if you don't want it in your face. I keep mine on my helmet all winter long. https://www.ovationriding.com/produc...-helmet-cover/
For riding, I like T-max gloves that I buy at Mark's Work Wearhouse. I get the men's smalls - not because I have big hands (they're actually pretty tiny), but because the ladies' gloves are never as warm as the men's for some unexplained reason. These work well - the leather helps with the grip and they are really warm. https://www.marks.com/en/windriver-t...color%5D=BLACK
I only wear them for riding - if you do chores with them, they won't last long as they're not work gloves. For chores, stretchy gloves with thick wool mitts are best. You can take the mitts off if you need more dexterity, then put them back on.
I also have full (top and bottom) merino wool under garments from Mark's. On really cold days, I wear them under my winter breeches and I stay reasonably warm.
I agree with you on the down coat. Good for chores, not for riding. I usually layer when I ride. Merino wool undershirt, then sweatshirt, then my puffy vest and finally, a fairly light top layer or my plaid wool jacket for colder days. Quite often I will peel off my coat during warm-up though, thus the puffy vest underneath. It's usually enough to keep my core warm.
You do need boots. Really good winter riding boots. No getting around those. If there's one thing you should splurge on, it's this in my opinion. Sooooo many riders try to get through the winter without proper winter riding boots, thinking they can just add warmer socks, but they're always complaining their feet are frozen. Don't do this. Get good winter riding boots. But be warned, they won't be good for walking around in snow or doing chores. Best to keep another pair of boots on hand for that. Just for brushing and tacking up it's fine though. And yes, of course you'll want wool socks. I prefer a nylon sock underneath, like a knee-high nylon I can put on under my wool socks. Make sure your winter boots are big enough to accommodate thick socks. If your toes are begin squeezed in the boot, they'll be cold.
Oh, and if you really want to go all out, and make riding in the winter an awesome experience, get yourself one of these riding skirts! The company who makes them is called Arctic skirt, and they are absolutely amazing. They wrap around your waist and fasten in the front with velcro (there is an adjustable string waist). There are velcro straps that go around your leg. My daughter and I love ours. Not absolutely necessary, but if you feel like splurging, you won't regret investing in one of these. https://www.arctichorsegear.com/coll...sulated-skirts