Hudson, unless you are very lucky, the carb heat is pretty useless for a restart once the engine has stopped. Both for the reason you state (cold muff) (oooer!) and because the airflow into the carb will be negligible.
Use the carb heat when it starts running rough or preferably before. If the engine stops, plan a forced landing and if you still have time, try a restart. Conducted heat from the engine block may have dislodged it after a minute or two.
Exercising the throttle may also help.
Opening the throttle wide before trying a restart wont help the engine due to providing an over weak mixture
I would still select carb heat hot even if the engine has stopped as you need all the help you can get and if it does restart it will melt the residual ice.
Best advice.....follow the flight manual.