While it may be possible, sometimes, to play videos or music in your hosted Windows Desktop, it is never ideal.
Stuttering audio playback
Stuttering video playback
Sound and video synchronization problems
Stuttering hosted Desktop performance
In general, you will want to minimize your hosted Desktop session and play the multimedia using your workstation PC or terminal.
Playing multimedia on your local workstation or terminal will eliminate extra network hops and give you the best 'YouTube Experience'.