I don't think dry ice is what you want. Airlines and the TSA are both understandably hesitant about having huge clods of solid carbon dioxide sublimating away in the cargo hold during flight.

As I understand it, the TSA limits dry ice to four pounds per passenger. And United will charge you extra for carrying it: http://www.united.com/page/article/0,6722,52830,00.html

That's $175 each way just for your dry ice. And four pounds of dry ice won't do much to keep two hundred pounds of moose (sorry, elk) cold.

So, yeah, water ice is the way to go. A decent cooler plus a bit of water ice should easily keep your meat good and frozen for the duration. Apparently there are no problems with taking a cooler on board, but I'd plan to show up at the counter early with the coolers plus a huge roll of tape, ask them about whether it needs to be inspected, and then tape it shut.