I don't know if it'd work in zone 6.  I guess you should find out how carrots grow in your zone.  If they're typically grown over winter or if they have to be harvested before a hard freeze.  We do get freezing temps occasionally, but the ground does not freeze and we only get snow once in a blue moon.  This winter the coldest it got was about 25 for 1 night.  The tops of the carrots looked a little sad after that, but they didn't die.  I would assume that if you plant them at the proper time for your zone, they should grow fine even in a contianer.  Although, if they do grow in the ground under snow all winter, you may have to protect the container in some way so it doesn't get too cold. 

As for the radishes, it was a total failure.  I planted them at the same time as the carrots.  I had read in a book that planting radishes with the carrots would help keep the soil loose so the carrots could grow better.  And that by the time the carrots started getting big, the radishes would be ready to harvest.  Well, mine all popped up very quickly, but when the radish part started to form, they started to push out of the soil.  The top half of the vegetable was sticking out of the soil, and it got all leathery.  So that's why I assume I didn't plant the seeds deep enough.  It's a little late to plant more.  I need to get those containers cleaned out and ready for my tomatoes and cucumbers soon.  So I guess I'll try radishes again in the fall.