Certainly shipping an elk home would be really expensive, but he asked about a mule deer. That is a whole nother subject. I always travel with an ice chest that just meets the size requirements (generally a 50 qt.) I check it as one bag and even put stuff in it going up there for more room in my other bags. A big mule deer can be easily quartered, deboned, and brought back in a couple of ice chests (one you take, and one you buy when you get a deer). Or if you have it processed and frozen, you will be able to bring it back in a single ice chest. Then the extra one ice chest will cost you as "additional baggage" (last time I checked that was $80).
The horns, which was really the question asked, is another question entirely. I don't think a good rack will fit "under the seat or in the overhead bin", so I am not sure how to take that as a "carry on". I am also not adept at caping it, so I take it to a taxidermist and have him cape it and package it since they do it all the time. Then you can either take that as "additional" baggage or have them ship it home for you.
txhunter58
venor, ergo sum (I hunt, therefore I am)