Non-paranoid solution: Ask an airport employee or check the airport's website.
Summary: While it's a good idea to be mindful about network security, joining the "official" WiFi network doesn't make your connection any more secure. Instead, use a VPN or stick to fully encrypted services, such as HTTPS websites. For more details, see the rest of the answer below.
If the network is open access and doesn't require a key to join, then all packets are unencrypted and absolutely anyone can sniff out everyone else's traffic. If there's a key, things are a bit more difficult, but likewise not secure. To quote an excellent answer from SuperUser.SE:
With WEP encryption, it's super simple. Everything's encrypted with the key you needed to know to get on the network. Everyone on the network can decode everyone else's traffic without even trying.
With WPA-PSK and WPA2-PSK, it's a little trickier, but not too hard. WPA-PSK and WPA2-PSK encrypt everything with per-client, per-session keys, but those keys are derived from the Pre-Shared Key (the PSK; the key you have to know to get on the network) plus some information exchanged in the clear when the client joins or re-joins the network. So if you know the PSK for the network, and your sniffer catches the "4-way handshake" another client does with the AP as it joins, you can decrypt all of that client's traffic. If you didn't happen to capture that client's 4-way handshake, you can send a spoofed de-authenticate packet to the target client (spoofing it to make it look like it came from the AP's MAC address), forcing the client to fall off the network and get back on, so you can capture its 4-way handshake this time, and decrypt all further traffic to/from that client. The user of the machine receiving the spoofed de-auth probably won't even notice that his laptop was off the network for a split second.
There is also an issue with the recently discovered KRACK attack, which makes it possible to decrypt traffic on unpatched clients even if you don't know the network's password. However, it's not too relevant for public WiFi, as everyone in the area knows the pre-shared key.
If we go beyond simple traffic capturing there are various MITM attacks including ARP cache poisoning, DNS spoofing, HTTP session hijacking, fake captive portals, etc. Some of them are possible even without running a rogue access point. And if someone does run a fake AP they might as well use the official SSID to stay undetected.
The only way to be truly protected is to use a VPN whenever you are joining an untrusted network or at least use websites with SSL to avoid someone sniffing out your private data. Using a VPN can also have the benefit of making sure you're always seeing the Internet as if you're browsing from home, rather than facing arbitrary censorship and regional restrictions on online content.