Depends on temps/weather for me, but I usually get the skin off as soon as possible and the meat cooling. Usually lay everything out on a light tarp and hang out for a while after everything is off the animal, flipping it a few times and getting a light protective tacky layer. If you load up a quarter in your pack as soon as you are done breaking an animal down, there can still be a lot of retained heat, which I try to avoid (especially with antelope).
I age the meat in coolers and don't usually hang it - more control over temp and humidity. When the weather is going to be right, sometimes, but rarely, I'll field dress the animal, leave it whole and hang it. Almost always anymore though where I hunt is a pack out proposition and I skin and quarter.
Long story short - skin off almost always to cool (fully) asap, and let 'pellicle' develop. Avoid loss by aging in coolers rather than hanging.
I am only speaking for myself and what has worked for me, I am sure other guys have other methods. I would try to leave the skin on if hanging, and make sure to take it off if aging in coolers.