I'll do 1 mile (1.6km) in just about any weather, but 4km I'd personally not do below about -20c (-1f). Then again, NWT folks are a different breed :-)

My go to bike for any commuting is a Dutch Opafiets which is what I ride all year. I put Schwalbe Marathon Winters (studded) on as soon as it snows. Having the entire drivetrain and brakes full enclosed is critical during winter for me. City Bikes | LocalMile

In extreme cold like that you can have cable freeze ups so I'd go with a coaster rear brake and roller front so that you'll always have some braking capability (coaster always works). Also stick to middle gears (4,5,6) on extremely cold days so that if your shift cable freezes you'll be in a good gear. On my Workcycles Omafiets (8 speed Shimano hub) I can ride anywhere in 5th gear.