✦ Space: The rider and mount both occupy the mount’s space. However, the starting location of the rider’s spells, attacks, and abilities do not change to the mount’s size. Whenever the rider uses an action that that requires accounting for a range to a point, the rider first picks where that square is located in the mount’s space, and the action uses that origin square as the starting point for calculating distances.
✦ Mounting and Dismounting: Once during your move, you can mount a willing creature that is within 5 feet of you or dismount. Doing so costs an amount of movement equal to half your speed. For example, if your speed is 30 feet, you must spend 15 feet of movement to mount a horse. Therefore, you can't mount it if you don't have 15 feet of movement left or if your speed is 0.
If an effect moves your mount against its will while you're on it, you must succeed on a DC 10 Dexterity saving throw or fall off the mount, landing prone in a space within 5 feet of it. If you're knocked prone while mounted, you must make the same saving throw.
If your mount is knocked prone, you can use your reaction to dismount it as it falls and land on your feet. Otherwise, you are dismounted and fall prone in a space within 5 feet it.
✦ Controlling your mount: You can control a mount only if it has been trained to accept a rider. Domesticated horses, donkeys, and similar creatures are assumed to have such training.
The initiative of a controlled mount that you do not own changes to match yours when you mount it. If you own the mount it takes your characters initiative when combat starts. It moves as you direct it, and it generally has three action options: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it. If the mount has other actions in the monster stat block you may add those to the list of actions available to the mount
✦ Independent mount: An independent mount is defined as a creature that is considered intelligent and is able to support a rider. It retains its place in the initiative order. Bearing a rider puts no restrictions on the actions the mount can take, and it moves and acts as it wishes. It might flee from combat, rush to attack and devour a badly injured foe, or otherwise act against your wishes. If the mount has other actions in the monster stat block you may add those to the list of actions available to the mount.
✦ Targeting the Mount and Rider: Even though the mount and rider occupy the same space, they are still separate creatures and are targeted separately. For example, an attack that targets only one creature can target either the mount or the rider, not both. In contrast, spells and abilities that target an area can target both mount and rider, since the two are in the same space.
✦ Provoking Opportunity Attacks: If the mount’s movement provokes an opportunity attack, the attacker chooses to target either the mount or the rider, since the two of them move together. If the mount prevents an opportunity attack through actions like disengage or the flyby ability the rider also gains from this benefit since it's considered forced movement for the rider.
✦ Forced Movement: If the mount is pulled, pushed, or slid, the rider moves with it. If the rider is pulled, pushed, or slid and the mount isn’t, the rider can have the two of them move together. Otherwise, the rider is dismounted and falls prone in the destination space of the forced movement. I.E. if you're shoved 5 feet you can move the mount.
✦ Teleportation: If either the mount or the rider is teleported, the other does not teleport with it. If the mount is teleported without the rider, the rider is dismounted and falls prone.
✦ Grappling while mounted: For the purposes of grappling the rider, the attacking creature may occupy any space adjacent to the mount. A creature may attempt to shove the rider off the horse, shove them prone or grapple the rider. You'll follow the same rules outlined in the players hand book for the grappling or shove action. While prone on the horse you
If a rider is grappled by a creature and the mount moves the rider must make a strength or dexterity save against an athletics check from the grappling creature or become dismounted. On a success the rider breaks the grapple. On a failure, the mount takes its normal move action and the rider is dismounted. When dismounted the rider must make a dexterity save, dc 10, or fall prone when dismounted.
If the rider is dismounted and falls farther then the reach of the creature that initiated the grapple and is to heavy to lift, the creature may let go of the rider ending the grappled condition.