Everything is possible. Makes only sense what's convenient and what's the price.
On Linux I expose only ssh secure port, and use text terminal from my phone via slow GPRS connection (for instance) to get work done.
On Windows I have to run GUI via fast link. I don't like the idea to expose RDP ports to the Internet, so I either have to use a kind of VPN, ssh passthrough, or use tools like TeamViewer. RDP has issues - miner sometimes can't read/manage temps/fans if started from remote session. Sometimes it works - I can't find out why and when. For miner there is absolutely no sense to run GUI to manage rigs.
It is a matter of taste, but Linux is also free and more stable, has a watchdog that can reboot it even if GPU driver hangs. Windows sometimes can't or require external watchdog device. Etc, etc.