Hi Hacksaw,
It is common to see foam insulation (usually Stryofoam SM) used as seat cushions in ice huts and on camping chairs. It also makes a very warm "toilet seat" and is what we have in both the outhouse at our cabin and portable "thunder box" for remote truck camping.
We have tried sitting on it while on the deer stand but it makes a loud "squeak" when you move on it. Standing on a piece while ice fishing helps heep your feet warm.
If you cut a hole through the ice and want to use the same hole the next day (for fishing or water collection) put a piece of thick stryofoam in the hole and cover it over with loose snow. Unless it is really cold overnight the hole will usually be unfrozen the next day.
Mike