I too have heard that the windpipe should be removed asap. Don't know if it is true but have heard it. The heart does not need to be pumping to drain main arteries and veins just gravity. if animal is dead and you are going to gut it immediately, then no there is no reason to cut the throat. One thing not mentioned yet is that if you are going to mount the animal NEVER cut the throat or your taxidermist will be very angry.