I have always hunted private land and we used to hang them in the barn to skin and cut them up. Looking back it was almost like a 3 ring circus compared to how I do it not. We would gut them, drag and load them into a truck, hang them up, skin and process them.
Now I drag them far enough I can drive my truck up to them. It’s almost like fileting a fish with them laying on the ground. I start with the front shoulder, do one side then flip it and do the other, you can skin it in portions you are working and if you cut the hide in the right angles you can peel it back and use it to keep exposed meat from touching dirt as you are cutting, I find it works best on the back strap if they are long and you are trying to get it all in one piece working alone.
I do the same thing, throw the meat in an ice chest then stop at the store and throw bags of ice on it. I leave it in an ice chest a couple days adding new ice and flushing out the bloody water. I am on a deer page where I have seen this method argued about it and what not, a lot of them add salt to the water. I have done this since before I read those arguments, I don’t add salt, but I do let the blood soak out in the water from the melted ice.
95% of the waste is left in the field for the coyotes. They usually won’t touch it for a couple days until my scent around it dies down but once they start, they clean it up quick. I have shot deer I was not able to recover until the next day and coyotes have gotten all the meat. If I have to leave one lay, I urinate near it and leave a coat or something with a lot of my scent draped over it, I have never returned to find anything eaten after doing that.