Ice is handled by studded tires
Darkness is handled by lights
If you can dress up to do any outdoors activity in winter you can also dress to ride a bike.
Really, weather is not a problem.
Really, that is wishful thinking. If you wear glasses, they always fog up. Face protection is paramount, leaving you looking like a serial killer. Massive gloves are required, since they are the most exposed. Then there's fumbling with the bike lock and key while wearing massive gloves, trying to fit your helmet over your hat, baggy snow pants caught in the gears, decreased visibility when in snow, ... They are all small things, but weather certainly IS a problem.