In some cases, when upgrading to the new PSM (v9.5+ with server 2012) you cannot use copy-paste
This issue is caused when the connection component you are using to connection doesn't have the Drive Redirection
To enable copy paste, under the connection component options
Administration > Options > Connection Components > [COMPONENT] > User Parameters > AllowMappingLocalDrives
You need to change BOTH the value AND visible to 'Yes' in order for this to work. (Changing only single one won't work.)
Note: Yes, to enable copy-paste in RemoteApp you will need to enable the drive sharing in the RDP.