Congratulations on the first bow deer. It's a totally different feeling IMO.
I wouldn't let it hang more than over night personally and I would skin it as soon as I got it home. The next morning I would pull the back straps, neck meat and anything else you want and put it in the fridge with the front and rear quarters. If I shot it in the morning I'd do it the same day. I wouldn't hang mine for a full day unless the high temps were low 40's max and preferably cooler.