Maybe it was the heat from all of the power plants. As we know when it is cloudy outside it holds in heat keeping it from cooling off as much as night. Maybe this is something of the same effect with the heat from the power plants being held in like a huge furnace. Keeping things just warm enough to prevent frozen precipitation.
I would have to say as long as the machines kept the power plants running and all of the fields of humans growing almost forever if not longer. It is stated in the first Matrix that a human produces 25000 BTUs of body heat. Between all of the fields and all of the power plants, that is a lot of humans putting off body heat. Then you have the thick blanket of clouds to prevent this heat from escaping.
I believe much of the earth would have been like this. I also realize that clouds are made of water in the atmosphere. With as much cloud cover as there was shown in the movie I would be willing to guess that the surface of the earth was possibly down to 50%.
Also with all of the power plants generating it is possible that they used water for cooling of the direct components as we do today. This would in turn warm a lot of water on a daily basis.
The other aspect to look at is that they did not exactly travel the entire earth's surface so it may be that the other side of the earth is covered with a sheet of ice but all the heat that is generated gives almost a campfire effect warming just an area within a few hundred mile radius of the machine city and the power plants.
But then there is nothing to say that the machines did not have really large *Electric heaters running somewhere around the fields with the idea to keep the humans from freezing on the vine so to speak. Maybe the cold was killing their crops and they have crop warmers of sorts.