We rarely skin anything until we are ready to cut it up... For two reason, one the way we pack elk out on horses we need the hide to pack with, and two I like elk meat, and like to get as much as I can. No sense in throwing away a quarter inch all the way around him... I was taught to deal with dead critters by my granddad who was taught by his and so forth. I have no idea how many elk he delt with in his life, but I'd be wiling to bet a few more than all of us combined...
If the day time temps in the shade are under 60-65 degrees you should be just fine. I think the key points which have been brought up about meat spoiling is to get them up off the ground, and open the neck up! I'm sure we could argue this till the cows come home, but its been our experience with oh... I don't know 3-400 elk that skinning is a waste of time and the meat will get dirty or hairy no mater how hard you try to keep it clean.
We open them up completely usually half em so you can drag the hinds up on a stump or rock or something to get air under them and also spit the pelvice so they lay "flat". The fronts can go sour quicky if you don't open them up though, this is even true in sub zero weather. The hide on the neck is very thick and the hair is long and insulates very well... but if you take the windpipe out, cut right up to his jaw and open it all up by skinning it back slightly you should be fine. Absolutely have to get the shoulders up off the ground. A good way to do it if its a bull is to pull his head all the way back and put the antlers up under him. That opens the chest up as well as gets the shoulders off the ground.
For deer... we do the same. Out of all those elk, I can think of only a couple that we lost the fronts on. One was a bull my brother shot, and shot up badly in the front shoulders. We're pretty sure this is the reason for it spoiling all that blood bone shards etc.
Another was a hunter who we took that packed snow in the cavity thinking it would cool it down quicker and he didn't get it up off the ground, result front shoulders sour... Snow is an excelent insulator... We even do so much as to clear the snow away from a freshly killed animal. Air will cool it quicker than it sitting in a snow pile.
Another hunter proped the bull up but didn't open the neck up... He figured since it was 20 below out it would cool off... well he found out half his elk didn't cool off to well...
And one other was again by guys that we had hunting with us, we told them how to deal with their elk if they got one down... they din't get them up off the ground and lost the fronts on thier bull. It was cold out as well, probalby in the 30's...