RE: field dressing IN THE FIELD?
Always have and always will where they fall.
Rick, the problem with trying to hunt the coyotes over the gut pile is that the likelihood of the coyotes coming in to eat while you're there. It may take them an hour, 2 hours, 8 hours, or longer to find the guts. So it comes down to how much time you're willing to wait! It would be more fun and more successful calling them with distress calls after deer season!
It won't take long for coyotes to clean up a single gut pile. If the coyotes are already in the area anyways, then let them do what they do best! Like RD said, lots of critters will benfit from the gut pile being left in the woods!