I think you have web proxies and HTTP/SOCKS proxies confused. You can install a script like Glype or CGIProxy on your website to use as a web proxy. An HTTP/SOCKS proxy would require that you have enough permissions on the server to install software which you most likely will not have with any free host or any shared host for that matter.
You're only real option is to install a web proxy script on your free host, however, I doubt the host you are looking at even permits those scripts. It would likely be removed pretty quickly I imagine due to the inherent liabilities they have.