As of May 20, 2014, Nintendo WFC has been discontinued.
This means New Leaf, which uses Nintendo Network servers along with 3DS and Wii U games, is sadly the only Animal Crossing title you can play online. You can no longer go to other people's towns in ACCF or ACWW via Nintendo Wi-Fi Connection, which is disappointing but unfortunately true.
There seems to be some confusion lately over this, as some members come back to ACC and want to play ACCF with others and aren't notified of the Wifi discontinuation. Hopefully this will clear up any confusion when Copper tells you you can't connect.
"Depart from evil, and do good; seek peace, and pursue it."