You should see them everywhere on the east coast between Nemuro and Rausu. They often perch on the beach, trees, concrete beach defences and atop streetlights etc. They are always flying about too. You'll see plenty.
It has been a very mild winter so far this year (it's raining outside as I type this but I live in the milder south of Hokkaido) but the cold usually hits in mid December, I'm sure Lake Furen will be frozen by the time you arrive. Lake Furen does have places where the eagles gather on the ice, if you stay at Matsuo's lodge at Furen-ko he will be able to tell you more details.
Don't worry you'll see lots of eagles. Also the Cranes/Eagles at Akan and the Owls at Rausu will still be there. The only thing you may miss if you come in January (as I said above) is the eagles on the sea ice from the boat trip at Rausu (unfortunately this would be the highlight of any winter trip to Hokkaido).
I attach a couple of shots from last weekend, even where I live in south Hokkaido it's easy to find and photograph them. You'll be fine in northeast Hokkaido in January.
