I to have been in that same situation, except I was not duck hunting either. My gsp ran out onto the ice and break through as well. I took a different approach. My dog was a pup when this happened so he didn't weigh much. He made it about 50 60 yards from the shore before he broke through. Looking at the ice I knew it most likely wasn't going to hold. Luckily for me it was just thin enough that I could break it as I swam out to the dog. It was swim a stroke, break the ice, swim a stroke break the ice for about 50 yards. Luckily it was a lake and not a river so no real current to worry about. The whole rest of that winter the dog would freak out if he even stepped on a frozen puddle in the driveway. There were times I had to actually carry him over little tiny frozen creeks that winter because he wouldn't go near them. He got over it well enough though.
This all happened at our hunt club. My dad was up in the clubhouse when I walked in soaking wet and freezing. Talk about catching an earful.