Any standard Linux installation is configured for remote use. The traditional way of using it is with the X Window protocol, which requires X software on the client (e.g. as distributed with Cygwin). An alternative is VNC. Modern Linux distribution also offer VNC-based connections as a standard option.
Setting this up for all of your users requires some Linux/X knowledge. I have no idea what Ulteo Server does, it may save a lot of configuration and troubleshooting effort. Similar offerings may exist from other vendors. But the basic capability of working remotely, with multiple users at a time, each with their own desktops on the same machine, is standard in Linux.
If you want to use the Remote Desktop Protocol built into Windows systems, you can do that on Linux: there are various clients (usually
rdesktop or some shell around it) and to get a server you can install
xrdp which builds an RDP server on top of a VNC server. I use both of these a lot to interconnect between Windows and Linux systems and even between Linux systems.