I would be concerned about them never getting into winter mode. They would consume huge amounts of stores and you would have to feed constantly. You might also confuse the bees moving them from inside to outside. The hive body would move, but the entrance they are used to using would still be there. General rule of moving a hive is 2 feet or 2 miles. Anything in between this confuses the bees. When trying to feed indoors, how are you going to keep the bees in the hive? I think you'd end up with a basement full of bees, and possibly a colony setting up shop in your rafters. Not good!
If the colony is on the weak side, feed, feed, feed in fall. Then wrap or insulate the hives when the weather turns cold. Keep them out of the wind! A good wind block is essential. Then make some candy boards and have them ready. In our area, with our cold, you might want to consider wintering with 2 deeps and an extra medium of honey stores. Don't wrap or insulate too much or you'll trap all the moisture in the hive and kill it with condensation.