I've seen
online that there are beekeepers in Greenland. And mead is a traditional drink in Scandinavia is it not? And it used to be colder there than it is now. So obviously it can be done. As for what the methods are.... *shrugs*.
Logically it seems that bees
should make less honey in places with long, cold winters as there are flowers blooming throughout less of the year. Unless bees in warm climates are just slacking and cold climate bees feel pushed to pick up the pace. Nature is like that sometimes but I doubt it's the case in this instance.
I'd recommend feeding them with some kind of sugar syrup. Commercial beekeepers do it because they're greedy and want all the honey for themselves. In your case I'd consider it more of a supplement to get them through the winter. I'm not saying take all the honey, personally I'd leave them some for their health. You could produce it yourself with sugar beets. Beet syrup's got to be better for them than HFCS.
Also, there are different types of bees, so you might want to look into them and maybe go through the extra effort to get some less common ones more suited to your climate. And there are a lot of different hive designs out there, some must be more suited to cold climates than others. I've seen a picture (that I can't find) of a bee hut sort of thing with multiple hives in it that could be closed up in winter to keep the wind and snow off of them and provide a second layer of insulation. I'd imagine that would be close to ideal.
Finally, I'd plant lots of things nearby to provide them pollen during as much of the year as possible. If you don't have a garden, get on it. Don't be picky and demand the honey be pure clover, although clover might be a good thing too. I've always liked the dark funky herbal honeys better, personally.