Blvette,
Yes, by the end of January the snow on the North Shore is usaully excellent. However, anything can happen.
As far as good places to stay there are many. Depends on what you are looking for. There are full service luxury resorts, nice chain hotels, mom and pop hotels and resorts, and some real inexpensive less than desirable places. In the Silver bay area alone there is the American inn, the mariner, Cove point in Beaver Bay, Maple leaf in Finland, Whsipering Pines, Wildhurst, and a couple of B&B's. As you head further up the shore there are more of the same, go to the Lutsen area and there are more lodging choices than you care to look at.
As far as trips, you can head up the gunflint one day, head up to ely another day, loop up into the forest roads for a day, lot's of big rides you can do for a day.