Microsoft offers a very cool function for RDP sessions, not limited to Windows Terminal Services on Windows Server, but also works for Windows 7/Vista/8/10 professional.
When you make the connection, if the correct drivers are installed on the server, your local printer (on your client) is made available to your Terminal Services (RDP) session. In many cases, this is done by Windows simply querying your workstation for the correct drivers.
In some cases, however, this does not work, for some reason. In those cases, if you can find the correct driver, install it on your Terminal Server (ie, your Remote Desktop Server). Some printer vendors offer the bare bones drivers, so all you need to do is install them on the server. In other cases, however, you will need to download the installer and unpack it. Many installers are simply compressed archives which unpack themselves into the users Temp directory, then execute the actual install program.
At this point, you have made your Server (I include the Pro workstations, if that is what you're doing) aware of the printer. It has the drivers installed. Now, delete the printer you just created. This will not remove the drivers, just the bogus printer you “installed”.
At this point, on your next RDP session, your local printer should be displayed as an option, generally the default printer, and you can print to this. Remember, you are sending a print job over the internet, which is generally much, much slower than a LAN, so printing large PDF's, photos, etc… can be very slow.
Sometimes, especially with multi-function printers, and especially with HP printers, you have to go even further. See Install HP Printers on Server for the procedure for HP multi-function printers.