I live in the nordics, while you can get chain lubes meant for extreme cold, negative twenties to thirties should be fine to ride using any lube.

Internal bearing lubrication is not a concern, same for shifters and brakes. Hydraulic breaks are not a concern, provided there is no moisture in the system.

Gloves are a must, of course, but I've several sets for a range temperatures, you can do just fine all the way up to pretty thick finger gloves. Some people here like to use three finger gloves to let some of their fingers buddy up.

Studded tires also make a huge difference. I can ride without them, but studs basically eliminate the most common way to fall without seeing it coming, your tires just sliding out from under you on smooth ice.

Though it doesn't help on loose snow thick enough the tire won't sink through to contact the ground. For that you need width and tons of tread.