There shouldn't be water laying in the pipe that can freeze, unless you have a trap outside somewhere, or your house is below freezing inside. Brrrr.
Possibly the water in a trapped-gulley at the beginnning of the underground drain might freeze. If your waste pipe is sealed into this drain that might cause problems.
I suppose it's possible that the water could back up 3 floors from a frozen gulley, but I've never seen that before.
How do you know it's freezing that's causing the back up? Is it a shared soil-stack?
Without actually seeing your pipe-runs, it's impossible to say.