You can do this. They are called "redirected printers".
Printer redirection is automatic when the local printer uses a driver that is installed on the server. When you log on to a session on a terminal server, or to a computer running Windows Professional or Server and Remote Desktop, any local printers attached to LPT, COM and USB ports that are installed on the client (local) computer are automatically detected and a local queue is created on the server. The client computer printer settings for the default printer and some properties (such as printing on both sides of the page) are used by the server.
When you disconnect or end the session, the printer queue is deleted and any incomplete or pending print jobs are lost. Information about the client's local printers and settings are saved on the client computer. On subsequent logons, the printer queue is created using the information stored on the client computer.
If a printer driver is not found on the server, an event is logged and the client printer is not created. To make the printer available, the driver must be manually installed on the server. If you are not seeing auto directed printers, then it may be that the driver is not installed on the server.
You can also manually redirect printers.
Printers attached to LPT and COM ports on the client (local) computer can be manually redirected, although manual redirection of printers connected through USB ports is not supported.
To manually redirect a client printer, contact your administrator and provide the name of your computer (or IP address for a Windows-based Terminal). The client must be connected to the remote computer during manual redirection.
After the initial manual redirection, printers will be automatically redirected during subsequent logons.
Redirected printers are available for use with applications running on the server. Redirected printers appear in the Printers and Faxes folder in Control Panel and are named in this format: Client Printer Name/Client Computer Name/Session Number.