The problem, as thewitt, points out is that the sending of emails is done using the SMTP protocol. This, by default, doesn't require any account name or password. When you're on your home network, your email service provider can identify you and so will allow you to send email. But when you're away from home, on another network, your email service provider has no way of knowing whether it is 'really you'. Since there have been many famous cases of users impersonating other people and sending emails purporting to have come from another person, most (nearly all) email service providers don't allow the sending of email from a 'foreign' network using the standard legacy SMTP protocol, whose origins date back to the dawn of the Internet era. In 'Internet language' this is known as the 'Port 25 relay problem'.
To be able to send emails from a 'foreign' network you need to switch to a more up-to-date version of SMTP. In your email settings you should be able to switch on a secure login option for SMTP called SSL. This newer protocol requires an account name (your email address) and a password (your normal email password) and usually uses port 465 (it's usually prompted automatically by the iPad). With that secure login, your email service provider can be confident that it's really you who is trying to send email from your account and all will be OK.
It's sometimes easier to setup a completely 'new' email account on the iPad with the receive email settings (POP or IMAP) being identical to the first account and the SMTP settings being the 'new' one with SSL. Once you get that working properly, you can delete the older account that doesn't have the SSL. SSL will work fine, too, once you get home, so there's no need to switch back to the older protocol at the end of your trip.
If you have any further problems, don't hesitate to get back in touch and have a great trip..
Tim