Hi again Bilojax.

With the dry suit and other gear I would get back into the canoe and bail it out.
Then if you want onto the ice just sit in the stern, pull your gear to you so your bow rides high and run the canoe up onto the ice.

Have you ever heard of the canoe races they run across the St Lawrence river during the winter?

http://race.fit2paddle.com/C2047168441/E20070131131733/index.html

http://www.lightmediation.com/blog/podcast/september/Quebec_Winter_Canoe_Race_365.pdf

edit
One danger with falling through the ice or approaching it from the water is getting carried under the ice by the current.

It might make sense to tie yourself to the canoe just in case, but that depends very much on the situation.

edot 2:
One river I used to go on would build up walls on the edge of the ice pans and ledges. If you were to fall in along that stretch of the river you might be trying to climb out over ice faces 3 feet or more high, and the water was fast.