My round trip to the supermarket is, I think, 3.7km. I walk it in the winter still but it's less enjoyable - especially if it's slippery rather than just cold (I live in nearish to Ottawa). Only a couple of times have I been really really cold doing it.
BUT. You'll be doing this when it's pretty much coldest out, it's almost twice as far, and presumably you won't have anywhere to rest/warm up on the way? And you *have* to go, every day.
By all means try it - but don't feel like a failure if you want to get the bus or drive.
I reckon you'd have a hard time doing it in an hour in the winter, on foot. Bike with studded tires would be better.