Client tools (such as SQL Server Management Studio) are shared features that are installed on every node of a failover cluster. When a node is added, they get installed on the new node automatically. In case the tools haven't been installed before, you can install them without downtime. By default, the regular installation procedure installs the management tools on the entire cluster (i.e. all the nodes).
On older versions of SQL Server (2008, 2008 R2), installation of the client tools on a node may fail during the pre-installation checks, right after the feature selection. The check states that an instance is already present on the node, of course, stating the obvious.
Apparently, this is a bug in the installation program, and it can be circumvented by performing a silent installation from the command line.
Note that this only installs the management tools on the node you run the installation on. If you need to have it installed on all the nodes, perform the operation below on each of them.
On the server, open an elevated command prompt, and cd to the root of the installation media.
To install the basic client tools, run this:
Setup.exe /q /Action=Install /Features=Tools /IAcceptSQLServerLicenseTerms
To install the complete SQL Server Management Tools, run this:
Setup.exe /q /Action=Install /Features=ADV_SSMS /IAcceptSQLServerLicenseTerms
No progress will be shown during installation, and it will take some time. When finished, the command prompt will be displayed again, allowing you to exit.