Where I normally hunt my Hogs, is far from any ice source. And every hunt isn't successful so packing ice for every hunt is likely to be wasted ice. If you have ready access, use it. IMO most of the heat you have to deal with in the first couple of hours is from the inside of the Hog and not the outside.

The vast majority of my hunts are at night, early evening or early morning. So the temperature is usually manageable. I gut them quick, prop open the body cavity (with a stick) so they cool quicker. I cover them in a wet sheet for transport, windows open or in the truck bed. The air rushing over the wet sheet helps cool them some.

Prior planning prevent pizz poor performance. I transport mine quick before it gets too hot out. I have access to a Refer big enough for a whole hog or Deer, I let it hang and drain for a day or more.. Trying to cut up game in the field isn't my thing, The few times I tried it the meat got dirty and it was a pain, it is a lot easier with the proper tools and working on a solid surface IMO. I use a door sized table top and a couple of saw horses for skinning and butchering. The table top (old solid wooden door) is saturated in Bee's wax. Cleanup is boiling water.