I think you can leave the skin on until morning, but you really need to gut and clean immediately so the smell of the dead intestines doesn't soak into the meat.

Be really careful not to puncture the gall bladder.

If you have to drag the carcass to a place to hang it up to work on it, you definitely want to leave the skin on until you get it where you want it.

I hope you did bleed it right away though. I do think that it's much harder to skin it later. I've waited overnight to skin a deer and it was incredibly hard to pull the skin off.