I think it is important to note that the first indication of carb ice in cruise flight should be the pilot noticing an uncommanded reduction in RPM (or MP in an aircraft with a constant speed prop). At that point the first action should be to suspect carb ice and apply full carb heat.
and select full power
A lot of instructors when teaching PFLs start the initial actions by waffling about speed for height, selecting a field planning, a circuit, making a call and by the time they get round to finding out why the engine might have stopped, guess what the engine is much colder. Is that going to help if it stopped due to carb icing?
Engine roughness partial power loss or failure on SE a/c with a carburettor should be immediately:
CARB AIR HOT, SELECT FULL POWER
Dont wait till the engine has cooled down!