What do you do for your hands and feet especially, and if you wear glasses, the inevitable frosting of them. Heck, if you don't wear glasses, what do you do for windburn?
I've biked as low as about -15C, though it's much more comfortable keeping it above -10 -- -5 or so.
Some heavier Thinsulate gloves were always enough for me. Maybe a pair of those thin fabric cheapies underneath.
Boots were just my regular winter boots. I think they all say "comfortable" down to -40C at this point. Comfortable is probably overselling it, but I still have all of my toes.
I don't remember my glasses ever really fogging up until I'd get inside. I don't like things on my face, so usually just a hat with ear flaps. Add a scarf for neck and lower face. Perhaps a beard helped too. It and my mustache have certainly frosted up.
When I was doing it regularly, those days just weren't common enough to justify doing anything special. I could generally keep the rides short which really helped out.
None of my cycling / running gloves cut it. I didn't get to buying heavier winter gloves last season. Layering gloves, using hardware-store work and waterproof gloves has also come up. Key is to combine insulation, a wind/vapour barrier, and possibly something rugged on the outside against wear/falls. I can't find the reference I had in mind, though this one is similar: <https://www.outsideonline.com/outdoor-adventure/hiking-and-b...>.
Feet aren't as much an issue for me, but insulated booties would be good. I have a pair, but they didn't fit over my most recent cycling shoes. I did find a lower-profile older pair recently, might get lucky with those.
I wear a Spandex balaclava, which tends to direct breath toward my specs. That's also a problem walking in cold weather (which I also do a lot of, particularly when my glasses fog too much to ride ;-), and I'm leaning toward over-the-specs ski goggles or something along those lines.
In general, I’m fairly waterproof.
-30C was pretty cold, especially moving, but rare enough I could dress for it and keep my body parts.
Snowstorms are always fun. Free physics lessons included. How much traction can you get? Whoops, I’m laying on the ground.
Thunderstorms and hail you might want to avoid.