I have a good number of clients of my Wine Merchant Business that are hunters and come down at least 2-3 times a year. 80% of those come with their own hardware. 90% of all those that do hire a local agent that helps them clear the process and do the paperwork when they arrive in EZE. It is of course possible to do this on your own but it depends on how much patience and time you wish to invest in the process. I know a couple of local agents that are actually private tour guides that know the ropes of the process and ensure a quick and prompt processing upon arrival. I can put you in contact with one of them if you want... just PM or email me for details.

Disclaimer: I have no horse in the private guide race, I just know a couple of these folks because they bring me their clients for wine & wine related services....

Below is a link for the Argentine Consulate in London with info on what you need to do to enter Hunting Firearms into Argentina. Even if you are not UK based, the paperwork and the red-tape will be the same... if you want to be 200% sure, you can go to the website for the US Consulate in NYC or Los Angeles or any other large US City (as correctly stated in the post above) and get the information there.

http://www.clond.mrecic.gov.ar/en/node/2414