Hey @DrowsyBoar!
What about this:
When horse is first mounted, PlayerCharacter (or player Controller, wherever your inputs are handled) gets a reference to the horse. Make a “Mounted” bool in that same place.
Make an event to accelerate the horse, and one to decelerate the horse, on the horse actor.
Where your A button is set up normally on your player/pController:
On Triggered: A branch directly after the event, checking “Mounted”. If false, do as normal. If true, however, Get your reference to your horse, and as Horse, do Accelerate event.
Same on Completed, but activate the Decelerate Event 