When a mounted target of Dissonant Whispers fails its saving throw, can it use its reaction to move the mount and itself away from the caster, or does it use its reaction to move on its own, abandoning the mount? The relevant text from the spell is quoted below:
The target must make a Wisdom saving throw. On a failed save, it takes 3d6 psychic damage and must immediately use its reaction, if available, to move as far as its speed allows away from you. The creature doesn’t move into obviously dangerous ground, such as a fire or a pit.
When this came up in a game I was running, I ruled that the knight could use his reaction to ride the horse away from the caster and continued the combat. I think RAW, though, the knight would have had to use his reaction to dismount and flee.
I've already checked the Mounted Combat section of the PHB (p.198), but it doesn't seem to contain any relevant ruling on this subject, specifically not with regards to controlling the mount outside of the rider's initiative.
Best Answer
The target must dismount (costing half its speed) and use the rest to move away
Spells do what they say they do: the target “must immediately use its reaction, if available, to move as far as its speed allows away from you.“ It says nothing about the mount so it doesn’t affect the mount.
Even if the target had some ability that allowed it to use its reaction to move the mount, it can’t because:
The only exception would be if they were on a mount that was so big that they could use their full movement and still remain on the mount.