There is no built-in support for media access outside the local network.
Generally speaking, the more entry points you have into your network (outside access), the more likely one of them has a security problem.
There are several ways you can achieve what you want. You probably know about ssh/scp and I think there exist a ssh-file system that allows you to mount a folder through ssh. Maybe http://ampache.org/
will do the trick, if all you need is access to audio and video. And there is always VPN, I think there was someone working on VPN support for LinuxMCE, but I don't believe it was commited/finished.
Anyway, those are the options from the top of my head...
Thanks for your tips sambuca.
So far I have two use cases when I am on the move.
1. Listen/view media on a remote computer. Ampache seems interesting for this one.
2. Upload photos and videos to my mce network, e.g. when I am on vacation. I did some research on your suggested ssh solution and found a free solution: http://dokan-dev.net/en/
. As a test, I tried to ssh to my core using putty. I can't get it to work, it seems like the core refuses ssh connections on eth0. (The core is connected directly to DSL modem, no router between).