Using Windows Azure Compute to host a proxy [Update]
If you have admin access, you can disable the Windows Firewall with just with this small command:
netsh firewall set opmode disable
That’s it! At this point it is working out-of-the-box! 
The downside is that it uses a not secured connection and basic authentication.
I invested some time trying to get a secure https connection working between my browser and the proxy but it just does not work (for me).
I was realizing, that I really wanted an VPN endpoint and not a proxy but I also decided to not work any longer on this!