In the snow and ice, there are TWO problems. One is simple traction in applying the power from the engine to the road (getting going and keep going.) The other is distributing the weight so to have the most control when driving. (staying on the road facing front when driving.)
Both are important, but sometimes we think of one but not the other. If I have to choose, I will choose control. I would rather get stuck than to loose control when driving.
I have no experience with a Camry, but I have driven a Celica and I would tend to believe the Celica weight distribution would not be helped by adding weight front or back.