I always found it better to pluck and draw them whilst warm , that way you don't have your hand in a cold clammy bird .
After the bird has been dead for 1/2 or so it still plucks fairly easily and if it is a tough old sod you can always skin it entirely then cut the breasts and legs off and use the carcass for a fantastic stock if slow cooked with onions , carrots and celery plus garlic etc. if you feel like that sort of stuff .