i have read several articles in the fishing mags that say laying a fish on the ice/snow is bad news. you know how ice cubes can stick to your lip some times, that is cause it freezes the miosture in you skin not deep but just on the surface. now think of how thin fish skin and eye membranes are and its easy to see the possibility for damage. also when it is well below freezing it is possible for the fish's gills to get frost bitten rather quickly, remember there whole body is not many degrees above freezing so it dont take much for small delicate parts to freeze and a fish with frozen gills is at a big disadvantage.
so if your going to release fish caught thru the ice, and you should, attleast some, do it quickly