As it is now, there is free airport wifi at EZE, you can connect for an hour or so and reconnect as many times as you wish.
The wifi network interface is in Spanish, English, and Portuguese, you'll be asked to accept terms and conditions, it is totally safe to accept as the service providers cannot ask for personal info or store any data as you use the network.
The wifi may be quite slow in some areas of the airport, the connection is strongest at the waiting areas across all 3 terminals.
Not only EZE but all airports in Argentina except Calafate, Ushuaia, and Neuquen have free wifi.
There's also free wifi across Buenos aires at public access points. Here is a list of all these public access points