The same weather system that had freezing rain warnings plastered all over Environment Canada's map of southern Ontario pushed all that mix of rain, freezing rain and wind into eastern Ontario and western Quebec overnight and into this morning. There were flight cancellations in both Ottawa and Montreal, and the icy conditions caused two Ottawa school boards to cancel bus service this morning (although schools remained open).
All of this miserable weather is due to a 'warm front' that is currently to the south of the Great Lakes.
[ Related: Freezing rain, snow hit parts of Eastern Canada ]
A warm front — so called because it is the 'front' of the warm air as that warm air moves across the map — separates (in this case) warm air to the south from colder air to the north. If you could take a cross-section of the air across the warm front, and see the specific dividing line between the warm air and cold air, it would look like a very long, shallow wedge, with the warm front on the ground where the wedge ends. The less-dense, more-humid warmer air rides up over top of this wedge of more-dense, less-humid colder air, and the water in that warmer air precipitates out.
The precipitation can stretch out far ahead of the warm front, and in the winter, the type of precipitation typically changes quite a bit, depending on how far away from the front you are. Way out ahead you get snow, since the water precipitating out of the warm air falls through a deep layer of cold air. This is what's happening in New Brunswick and Quebec. As you move closer to the warm front, you are moving closer to the tip of the wedge, so the layer of cold air becomes thinner and thinner. You will keep getting snow until you get close enough that the rain falling into the cold air will only have a short time in which to freeze before it hits the ground, and so the snow changes to snow pellets and ice pellets, and eventually the layer of cold air is too thin for the rain to freeze at all. It falls all the way to the ground (or building, or car, or you) as rain, but the surface it hits is below zero degrees Celsius, and likely has been for several hours at least, so it freezes upon impact, accumulating as ice — freezing rain.
[ Related: Southern Ontario gets first bout of winter ]
It looks as though southern Quebec will get the several hours of freezing rain before the precipitation stops overnight. However, the weather system looks like it pushes northward once it gets into the Maritimes, so after New Brunswick gets its share of the freezing rain, the warm front will actually pass over the province, bringing warmer temperatures with it and changing that freezing rain to rain overnight and into tomorrow morning.
You can keep updated on Environment Canada's weather warnings on their website.