To chime in on several previous posts -

Way too many of my elk are killed in the most impossible places you can imagine.

I have frequently quartered with the hide on because I was going to be dragging quarters over deadfall, skidding over snow (or even dirt), or just because circumstances were that I had to get moving as soon as possible.
Under those circumstances I remove the hide as soon as is reasonable.
Normally I wouldn't choose to do it that way and the benefits of cooling w/o hide are important but it is choices and priorities.

On those few where I have quickly cut all of the meat off the bone for transport in those situations I really felt like those were some of the worse eating ones. I try not to do that unless I have to.