One of the most asked features of .NET 4 is the ability to install on Server Core OSs. I am pleased to let you know that you can now do this with a caveat. You must be running Windows Server 2008 R2 SP1. So you must upgrade your server to SP1 before installing .NET Framework 4 Server Core Profile.
One other thing to note you must also turn on .NET 2.0 support as well as WOW support. While we are installing the Full Framework be aware that not everything will function on Server Core for example WPF and ClickOnce do not work on Server Core.