Most of the advice here works in some circumstances. Trouble is, your degree of success is going to depend on how you are connected at the moment, how they set up their servers, who your mail host is, how they set up their servers. Ya, webmail works, but if you're like me and have more than one address, that can be a pain.
I travel a lot, and have this problem in hotel rooms but also at a lot of other places, too. Client sites are particularly difficult: they almost always have security rules that prevent me from doing my work.
What I needed was something I could set up and that would work in any hotel room and behind any firewall.
I found Loapost
. I've been using them for quite a while, and I love it. It's cheap (99 cents a month for me), so I just set it up and let it run. Not once have I had to re-configure it, no matter where my laptop sits. This is WAY better than webmail, or than fiddling with ports and authentications every time I move.