Yes. It does freeze over pretty consistently. I've hiked the shore for years at places like Pointe Mouillee, the Woodtick Peninsula and Pointe Aux Peaux and I honestly can't remember a recent year in which it hasn't frozen pretty much completely over.
Erie, btw, is the most likely of the Great Lakes to freeze over. It has less water than any other Great Lake and that means it gets warmer in the summer and colder in the winter than any of the lakes. If you want to see something cool, hike out to the tip of Pointe Mouillee on a zero degree day in January. It is what I imagine hiking through the Arctic is like. But it is VERY cool. One time I saw three tugboats clearing ice for freighters at the Detroit River Light.
You mention the power plants and they are a whole different animal. The warm water discharges at Fermi, DTE and the Erie Whiting plant generally stay open the entire winter. That means that many area birds congregate there.
Occasionally, if the winds are right, a giant shelf of ice will break from the North side of the lake and crash into the ice shelves on the south side of the lake. The result is kind of like plate techtonics. You'll get massive uplift in the ice and many interior ice caves.