Go all in and do what I did.
Buy a velomobile.
1 -Fully enclosed drive train, so rain, snow, etc don't affect it. Still have to hose off the wheels and other metal parts when they start salting the roads, though.
2- Three wheels, so it can handle a little slipping and sliding in much more treacherous conditions than a typical bike.
3 - Fully enclosed (not shown with 'race cap') which makes it reasonably comfortable at much lower temperatures!