Anyy decent size chest cooler (56 qt or so) will hold a boned out prairie goat. I wouldn't go to the expense of a Yeti. Heck the cooler would cost more than the tag! Bone him out and put him on ice on the cooler. When you get ready to leave drain out any water and remove the ice and put 2 or 3 chunks of dry ice in the cooler. You can cape the head and put the cape in a ziploc bag and toss it in the meat. Horns don't require anything special to drive home. Toss them in the back of the truck.

I grew up in CO and spent a lot of years stationed in VA with the Navy. I used to go home after deer, elk and pronghorn as much as I could and that is how I hauled meat back to the east coast.