I wouldn't fish any part of the river south of lockport. I think its always sketchy ice
We snowmobile on the Assiniboine from Headingley out past Elie all winter. Ice seems to be fine but we never head out before the end of December.
I would not trust the ice as much from Headingley into the city to the forks.
We have only ever seen a few places where holes were augered. Water tends to be pretty shallow in many parts and there are lots of rocky areas that would chew up your auger quickly. So be careful of the ice and be cautious where you drill.