Connect to Ubuntu Mate Desktop from Windows 10 or Server 2012

You're outside my area of knowledge now, but the question is more clear for others to answer. As far as I can tell from a quick search, regular ubuntu has a rdp server installed and ready to enable. Not sure if U-Mate does, though.

You probably know this already, but you need a server daemon installed and running on the Raspberry Pi machine. xrdp is one common option; am sure there are others.

I also found this older post on this very forum which may be of help.