If all the walls have a southern exposure, you could only be in one place. You are in the north pole.Therefore, the bear has to be white. The only kind of bears up in the north pole are polar bears, since it’s incredibly cold and the polar bear has adapted for that environment. Depending on the light of the day, the bear could look a golden yellow, but otherwise, it’s going to be a white bear.
If the walls had had multiple exposures, brown could be an answer as well for the actual color of the bear. If it’s dark outside, the bear might look brown or black, depending on how well the darkness is covering their fur and eyes, which are dark brown.