If you are going to haul your deer or hog to a locker plant or over the road to your house (depending on how far) you have two choices. #1, remove all you want without gutting and put on ice or #2 gutt the animal, ice in cavity and wrap in tarp and haul.
We do not need the ice. I gutt all of my animals and hang in cooler. They are usually at 33-35 degrees when I start the haul back home or to locker plant. I do wrap them in a tarp to keep road dirt off of the meat.
As far as field dressing, we used to gutt on the spot. However, since we have running water, a gutt dump, a walk-in cooler and a processing room (when we have time), we gutt at the house and haul gutts off.
Since my place is 45 minutes from my house, if I kill something on a Sunday evening, I can leave it in cooler until the next day, then I go back after work and haul to locker plant.