It appears that you are using the Deploy Printers feature of the Print Management console. This makes an entry in your GPO that tells clients to connect to a printer located on a print server.
If you have a separate print server, then you never needed the printer to be connected to the DC in the first place. If you don't have a print queue shared out from a server, then you'll need to make a queue on a server and share it. Whether or not it's on the DC is up to you. If that's your only server, you have no choice. I do recommend a separate print server whenever possible, though.
Do I need to keep that printer installed on the server?
You need it installed somewhere central.
Is that necessary?
If you want to deploy printers using the Deploy Printer function of the Print Management Console, then yes. Having queues reside on a server allows you to centrally manage and audit all documents send to all printers. It makes maintenance and management a breeze compared to having each printer mapped directly via TCP/IP to the printer.
Isn't the logon script creates the printer to everyone? Including the DC?
That depends entirely on what GPO you deployed the printer to. It will only apply to the OUs that the GPO is linked to. If you deployed it to the Default Domain Policy, then it will apply to anyone.
Side note: You really shouldn't be installing printers on DCs if you don't have to. Print drivers are the devil, and the last thing that you need on a DC is stability issues. You also shouldn't be modifying the Default Domain Policy unless you really know what you're doing. You should be making new policies and linking them to the appropriate OUs.
