I don't use Studio One so I don't know. I use Cubase 8 and I can.
If you can't drag and drop MIDI from your host, there's a trick to get MIDI from the host into EZdrummer 2.
Remove all MIDI from the song track in EZdrummer 2, then press the record button (below the track) in EZdrummer 2
As soon as you start playback in your host (with MIDI on the EZdrummer 2 track), EZdrummer 2 will record the notes being played from the hosts MIDI.
Now you have the MIDI inside EZdrummer 2. Edit it and then drag it back to your host.