The key phrase here is the "user agent" string.
For Firefox, there is a plugin that gives you a little menu to choose.
In Safari, use Safari Enhancer, PithHelmet, or any other Safari utility to enable Safari's debug menu. In it is a User Agent submenu to choose one of a few options.
As for your webmail: it might work on a non-IE browser, but it also might just rely on Windows-specific things. So don't be too surprised if you get weird behavior (if you get anything at all) when using Safari or Firefox to access the IE version of the page.
tooki