I don't live in a snowy country (anymore), but have climbed various snowy Australian mountains in specialist outdoor thermal pants which are super warm, water repellent and breathable - and, I can ride my horse in them when we have a lot of wind chill combined with drizzle, that would soak ordinary riding pants.
These are the pants:
They are microfibre fleece pants and don't have seams that are a problem for riding. They fit very much like tights, but slightly looser. The pants we wore came in two thicknesses; I've ridden in both - the thicker type is the warmest - I've never been cold in thick microfibre fleece mountain hiking pants - not even when I fell into water and got saturated and had to hike another 2 hours before getting back to the car park. If you fall in a lake etc, just wring the pants out and put them back on - they still keep you warm, nearly as well damp as when dry! (And don't ask me why I fell into water!
It was embarrassing!)
Gloves made from the same material are also great - I use them for hiking, and riding when it's cold. The material is soft, thick and lightweight.
You can also get jackets made from this, and I've worn those riding as well, but would probably put a sleeveless water-repellent weather vest on top of that too riding in really cold weather. Like this one:
It wasn't super-cold the day I wore that, so I'm in ordinary clothes under it. I was just interested in keeping my core warm. The nice thing about these vests is that you don't end up with bulk around your arms, which is a bit of a pain when riding.