I always worked from the other end, starting at the ankles of the hind legs and working my way to the head. No particular reason, that's just how my father did it and therefore how he taught me.
I doubt it makes much difference, really.
ETA: After thinking about it for a few minutes, it occurs to me that my father liked to occasionally roast and eat the heads. That more or less rules out cutting off the head as a first step, so that's probably why he did it feet-first.