As someone that has used the Assiniboine in both summer and winter I can say that there are spots on the Assiniboine that are quite deep. Going through the ice at any depth in cold temeratures would be a bad experience at best.
I haven't been on the river this winter, so I can't say if it's safe or not. We had a warm extended fall season and now we have a heavy snow cover. Both of those conditions can lead to less ice than normal. If you're going to use the river for recreation, be careful where you go until you know for sure it's safe.