I brought the dog ice fishing, and I pushed the dog in the hole in the lake's ice
That is mean, and dangerous for the dog.  What happened?
The water was freezing cold
Your dog didn't deserve that at all. They trusted you and came to have fun fishing alongside you, and you betrayed them just like that by pushing them into a dangerous, cold, icy hole. They could have drowned or died from hypothermia.
It's a small town dog and needed to know that ice wasn't safe
That wasn't a sensible way to teach the dog a lesson.  You have emotionally traumatized your dog, and for no good reason.