That's what IMAP is for. If these are computers you don't directly control, then I'd say any downsides of using gmail pale in comparison to the security implications inherent in your usage model.
[edit] Can't say I understand the negative downvotes. Maybe I inadvertently denigrated people's preference for webmail over mutt/mail.app/etc?
Regardless, the fact is that if you're utilizing webmail for remote e-mail access on shared computers, then there are much more significant risk scenarios at play than those of gmail.