The idea for this came from the way horses are handled in Mount and Blade.
Horses should gradually build up to a target top speed and then take time corresponding to the speed to slow down and eventually stop.
Horses should not be able to make really sharp turns while at a high speed, but should rather make changes at a more gradual pace towards where the player has clicked, creating more like a turning circle while moving at a very high speed. The turning circle would lower with the speed the horse is moving at.
A be a stun time of a couple seconds with an animation of your horse reeling if your horse runs into something while moving at a high speed.
Some time and an animation for turning your horse to face different directions.