You can go on thinner ice if you spread your weight out over a larger footprint, such as using snowshoes.
When I was a teenager, the fishing on the lake was HOT. There was about 5" of ice on the lake. A warm front came thru with rain, turning the lake into honeycomb ice. We had an aluminum jon boat. I put the boat on the ice, stood in the back of it, and slid it out on the ice by using an ice spud to shove the boat along. I caught many fish that day thru the same holes I was using before the rain came thru and messed up the ice. The boat spread out my weight enough so that the ice didn't even sink enough to bring water up on top of it.
I can't even imagine what people were thinking if they saw me out there!!!