Confirm that the Windows 10 computer and the Server 2003 box are properly connected on the network and can communicate with each other. Check firewalls and network settings to ensure there are no communication barriers. Check the Remote Desktop settings on the Windows 10 computer. Ensure that printer sharing is enabled in the Remote Desktop Client settings. Open the client, click "Show Options," go to the "Local Resources" tab, and make sure "Printers" is checked. If the built-in printer sharing doesn't work, you might consider using third-party tools specifically designed for printer sharing over Remote Desktop. These tools can provide more compatibility between different Windows versions.
Remember that older operating systems might have limitations when interacting with newer systems, so exploring alternative solutions might be necessary in some cases.