It would be difficult. The FaceBook app is not going to send your password or username insecurely. The biggest risk in a public wi-fi system is the public. Shoulder surfing and/or other social engineering.
The second biggest risk is man-in-the-middle attacks. This is where someone sets up a wi-fi network pretending to be the main network. It's difficult to intercept things like passwords (as long as the site uses decent security), but a lot of your other information may be sent in the clear. It depends on the site and/or app.
To be prudently secure in a public wi-fi network you should do two things.
One, be aware of your surrounding.
Two, use a VPN (Virtual Private Network) solution. I've heard good things about
Cloak. VPN creates an encrypted tunnel between you and your destination. Nothing the local network sees is in the clear.
To be supper secure, use a cellular connection and a VPN. While cellular is also susceptible to man-in-the-middle attacks, the equipment and knowhow are rarer than wi-fi attacks. At least so far. It's getting easier and more popular.
Which reminds me, I've been intending to test out Cloak for myself. Normally, I just avoid doing any sensitive browsing off my home network. But then again, I don't consider FaceBook sensitive. I don't put or post things I care about there. At least things that aren't available in half a dozen other places.
