If you want to stay in one place, you have to either travel over the ice (which you don't seem to like), under it (a terribly gloomy lifestyle), or through it (which has certain engineering challenges which I will now address).
I found an interesting reference book, Basic Coastal Engineering
It says that a vertical wall at the waterline can experience horizontal forces on the order of 200 to 300 Newtons per square centimeter. If you assume ice up to (for sake of argument) 6 meters thick this gives an overall force of something like 1700 tons per meter of width. This would take a pretty amazing amount of anchoring.
On the other hand, inclined plates can lift the ice, causing it to crack under its own weight and greatly reducing the horizontal force - for sake of argument, call it a reduction to 40 N/cm^2, or about 225 tons per meter of frontal width, which is much more tolerable. You need enough buoyancy to lift the edge of the ice, and enough depth to reach beneath it.
I think this would translate into something like either a long, narrow, very deep-draft barge or a SWATH-ship design (catamaran with thin vertical hulls standing on submerged pontoons). The barge would require more anchoring, but the SWATH has less reserve buoyancy. In either case, you would still need to occasionally deal with unusually thick ice, ie pressure ridges. This is probably best done by a watch force armed with depth charges or torpedoes - an underwater explosion is much more effective in lifting and shattering the ice. (Maybe replace the explosives with some sort of reusable high-volume compressed-air injector?
On the whole, this seems like a very large capital expenditure for very cramped living space. I think it is much more likely that people would live in portable (sliding) modules in a continuous migration against the ice movement, as suggested by James, or simply go with the floe (pun intended), as per bowlturner.
You might find Project Habakkuk interesting; this was a WW2 plan for an iceberg airfield stationed in the North Atlantic and prevented from thawing with a mixture of insulation and refrigeration. So long as the ice surface stays below -16C it will remain viable; in testing, 9m x 18m block was maintained through the summer by a 1hp motor.
In practice people would migrate to a far-North floe and construct a new town; ride it wherever it goes for the next 30 or 40 years until it becomes too expensive to maintain the refrigeration; then repeat the cycle.