This is because it is easy for someone to deliberately send thousands of spam messages (or someone who has a virus infected computer that does the same thing) using the hotel's WiFi, resulting in the Internet Service Provider of the hotel suspending their service.
This blocking of email ports is very common. Webmail is not affected as this uses a different port for the web browser, and it is not easy to make lots of automated mail from webmail.
So the answer is to use webmail. In some hotels, in addition to their free WiFi (that anyone who goes into their bar can use) they offer a paid WiFi service with higher speed and without email ports be blocked. This is normally available to registered customers and is less risk to abuse.
This WiFi port blocking will also affect your mobile phone. When this happens, you can disable the WiFi on your phone in order to allow it to communicate correctly with the cellular network.
