*** Improved by Wrobinson on 03/16/2008 ***
Your Windows network is operating in a workgroup model. The information provided by MrDenny below, as it applies to this model is correct. The reason that I am updating this answer is because Window Storage Server cannot be a domain controller. You need Windows Server Standard, Enterprise or Datacenter to install Active Directory. The latter is only available from OEMs.
Since you only have one Windows server and four client workstations at the moment, using the workgroup model is still practical but it does not scale well past 10-20 computers in which case a domain model is recommended for centralized access and administration.
*** End update ***
Active Directory provides for global authentication across all the machines. Active Directory (AD) is a very large system but would allow you to do what you are trying to do.
As all the users use a single username to sign on to all the machines AD isn’t really needed. If you wanted to use seperate logins for each user then AD would be handy as you won’t have to create seperate accounts for each user on each machine.
What you should need to do with the server is create a Windows Account on the Windows 2003 server with the same username and password as the XP machines use to sign on. This will give the users access to connect to the Windows 2003 server. Share the folder on the server that you wish the users to have access to, and grant the local account rights to the network share. When the users try to access the server it will pass the credentials from the XP machine to the server to grant the users rights to the server.
If the passwords on the workstations are changed then the password on the server account will need to changed as well.
I’d recommend that you setup AD on the server, and join the XP machines to the domain, and create user accounts for each of the users within Active Directory, then grant the domain user accounts read access to the network share.