As an update, Delta which was historically the only US airline operating out of EZE that would have on & off issues with full cases of wine seems to have gotten its act together. Ive had a good number of US based clients of mine fly out on DL over the past few months and they have all gotten zero issues from the Delta check-in counter. As long as the wine is properly packed (ie. Styrofoam boxes), you will have zero issues.

United and American have a history of being very "wine friendly" here at EZE, so its business as usual for them.