Yes, it is possible in general with Go, I'm not that familiar with Martini specifically. The http response from calling the remote file returns a Reader
interface, and your request handler has a Writer
interface. This means you can read a stream of data, and write a stream of data. Making your responsibility only to manipulate what you want, and "patch" the forwarded stream to the request stream.
Go even has a ReverseProxy
utility built into the standard library:
http://golang.org/pkg/net/http/httputil/#ReverseProxy
You can probably mix Martini and the standard http library if you want.
[EDIT] Reading the martini docs, you can add raw http handlers like the standrad library has, meaning you can indeed do that: https://github.com/codegangsta/martini#service-injection