The description of Ashardalon’s Stride spell reports:
3rd level transmutation
Components: Verbal, Somatic
Duration: Concentration, up to 1 minute
The billowing flames of a dragon blast from your feet, granting you explosive speed. For the duration, your speed increases by 20 feet and moving does not provoke opportunity attacks. When you move within 5 feet of a creature or object that isn’t being worn or carried, it takes 1d6 fire damage from your trail of heat. A creature or object can only take this damage once during a turn.
My question is, how does this work when you’re mounted? Does the horse gain the twenty feet of movement, and it just carries you along with it? Do you have to dismount to use it? Do you shoot off your horse because of the explosive force of the spell?