In theory, yes. Wifi encryption (if present), only protects data sent from your PC to their access point. After this it is sent without additional encryption so messages could be read and captured if the Wifi owner really wanted to do that. In practice, even capturing unencrypted data and reading it requires a higher level skill, beyond the regular systems administration skillset. If you're a spy or access personal banking information you should worry about it and avoid using untrusted Wifi without additional encryption like a VPN. If you are just posting social messages, chances are no one wants to try hard enough to read them.
In addition to possible Wifi encryption, your applications could be encrypting your login, password, and the data as well. For example using an HTTPS browser URL means the data is encrypted between your PC and the system that serves the page, regardless if Wifi provides any protection. Encrypted data can be captured but not read, in most cases. If the URL starts with HTTP then there is no encryption and Wifi owner could eavesdrop on your messages. On top of that, DNS queries which reveal which sites you visit will be visible.
Wifi Encryption relevance:
WEP: extremely easy to crack
WPA: easy to crack
WPA2: cracked in 2017 but patched Access Points should prevent most of the risk.
When applications don't use the browser the question is harder to answer. You should research if your non-browser applications encrypt credentials and data and then you will know if Wifi owner has any means to capture and read your messages.