I hang them with the head up. I don't want fluids collecting in the neck area. Also I think they are easier to skin this way.

On that note, I did the golf ball skinning technique on the last deer. It worked pretty well but I had to slit the skin on the front legs (I was told you didn't have to). I don't think I would have had to if I had some stronger rope but all I had was clothesline rope and it kept breaking until I slit the front legs. Other than that, it peeled the skin off in less than 30 seconds.