TFS 2012 introduces a new concept called local workspaces, which differ subtly from the behavior of workspaces in previous versions of TFS (the old default behavior is now called a server workspace.) Local workspaces do not require read-only files and instead allow files to be edited without checking out from the server, and they are intended to be more suitable for small to medium sized workspaces. For this reason, local workspaces are the default in TFS 2012.
Local workspaces, however, are not compatible with TFS 2010 and TFS 2010 clients will not be able to use a new local workspace.
You can convert the workspace that you created with your VS 2012 client to a server workspace. In the Edit Workspace dialog, select Advanced, and you can change the type from a Local to a Server workspace.
At that point, you should be able to connect with VS 2010 and choose that TFS workspace.
(Note that it’s not sufficient to use tf workspaces as that will return a cached copy of your workspace list – you will need to connect to the server either with Visual Studio 2010 or with a tf.exe command that talks to the server.)