It's not easy but it's doable. Actually, it can be quite fun because you'll often find yourself riding around comfortably in a winter wonderland when no one else is around because it's too cold for them( but not for you since you're dressed accordingly)
I go out biking here down to about -30 but usually no more than 20 km distance.
The trick is to have a MTB that you really don't mind abusing and hitting up a thrift store to stock up on walls of wool. Better to be too warm than too cold, especially if you ever wander far from home. I usually wear three layers of everything but it depends.
I think hands and feet are the most crucial to keep toasty at all costs.
You move much slower but it's a lot of fun, especially if it's snowing out.
Another thing is to just accept the fact that you're going to slide out and fall quite a bit. It's not a big deal - you're already going slow because of the snow and the winter clothing is basically body armour.