One way to prove or disprove that it's the hotel, if you can, take your iPad to some open wifi area and try to get your mail. If it works there but not in the hotel then it strongly suggests that it's the hotel's setting.
I do know I had something similar where I was on AT&T hotspot and couldn't download my mail via the mail app, but it worked fine via web access (using mobile safari).
Using web mail might end up being a work around for you since, if it is the hotel's setting, your chances of getting them to change is are very slim.
iOS: Unable to send or receive email
Can’t Send Emails on iPad – Troubleshooting Steps
Setting up and troubleshooting Mail
Server does not allow relaying email error, fix
Why Does My iPad Say "Cannot Connect to Server"?
iOS: 'Mailbox Locked', account is in use on another device, or prompt to re-enter POP3 password
Configuration problems with IMAP e-mail on iOS with a non-standard SSL port.
Try this first - Reset the iPad by holding down on the Sleep and Home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons. (This is equivalent to rebooting your computer.)
Or this - Delete the account in Mail and then set it up again. Settings->Mail, Contacts, Calendars -> Accounts Tap on the Account, then on the red button that says Remove Account.