Depends, some bins are designed to be left outdoors. With enough heat and organic matter to prevent total freezing a bin outdoors wlll be fine. A small tub however will freeze and kill the live worms. I have had an empty outdoor bin above ground refilled with horse manure and some time after filling I spotted some red wigglers. Probably egg capsules left in the corners survived and hatched. Who knows!
I'm in zone 6B and have my worms in a 3-tier 23gallon plastic storage bin set up. I plan on digging a ditch and burrying the whole thing all but an inch or two above ground to keep a lid on to over winter it. I've read that as long as the worms are under the ground freeze level, (about 12" or so at worst here in TN) that they will live and thrive in the cold outside. This is my first year vermicomposting so I'm not sure this method will work but I'm going to try it out.
My bins are rubbermaid plastic storage containers. I am going to keep one in my insulated but not heated garage and see how it does. A second one I have already brought inside. It is inconspicuous and does not stink. I haven't had any issues with it and it's been inside for about a month. It's actually nice having it right there inside because I don't have to trek out to the garage to feed the worms.
I had a successful inside bin, homemade from a Rubbermaid 10-gal Roughneck, for a year. I had read about people in apartments having inside bins, and figured if they could do that, then I could. I live alone so I didn't have to get any kind of approvals. The bin did not smell at all and did not attract flies, and, as seran said, was easy to feed and to check on. I am not concerned with freezing but of baking in the hot, hot summer. Now might be a good time for you, nanners, because it will give you a new gardening activity for the long winter, and you will have castings to add to you seed starting for next year's garden.