As you may know, Server Core installations of Windows Server 2008 R2 now support the .NET framework.

But, some functions are not available on Server Core. As Server Core only has a command prompt and no GUI, mostly Graphical User Interface objects are not supported.

For a list of the .NET 2.0 features, excluded see here
Additionally for .NET 3.0/3.5 see here

Also remember that installing products like SQL Server 2005/2008/2008 R2, Exchange Server 2003/2007 , SharePoint Server 2003/2007 and others are not supported on Server Core. If a Server product supports Server Core installations, it will be clearly documented. If nothing is said, you need to assume it is not supported.