Mounted Combat

Mounted Combat is a mess and kind of spread out. This isn't really a ruling as me trying to gather all the rules in one place.

What is a mount?

A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount.
-PHB pg. 198

• A willing creature: The creature must be willing. There are no rules for riding unwilling mounts, but if you're especially daring you could try to "grapple" something larger an mount it. Results may vary.
• At least one size larger than you: Horses are large, and mastiffs and ponies are medium. Those are the typical mounts.
• That has an appropriate anatomy: It's a little subjective, but if you're really curious just ask.

Mounting, Dismounting, and Forced Dismounting

Once during your move, you can mount a 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.
-PHB pg. 198

• Once during your move: You can only mount a mount once, and it takes place as part of your movement for the turn. So no using your movement to jump between multiple mounts in one turn. “During your move” is a bit of a weird phrase since there is no distinct “move” part of the turn in 5e, but it just means that it’s part of your movement and not an action of any kind.
• You can mount a creature that is within 5 feet of you: The mount needs to be within 5 feet regardless of your size, its size, your reach, etc.
• or Dismount: All of the same rules for mounting a mount apply to dismounting; movement cost, etc.
• Doing so costs an amount of movement equal to half your speed.: If you speed if 30 feet, it costs 15 feet. If your speed is 25 feet, it costs 12.5 feet, and you may have 2.5 feet movement of movement which is unusable at the end of your turn. If you're grappled or otherwise have your speed reduced to 0, no mounting for you.

• If an effect moves your mount against its will while you’re on it: This can be any number of effects: Your mount could be grappled or shoved, it could be hit with Thunderwave, or it could fall. These are dangerous possibilities, especially if you’re on a flying mount.
• 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.: just highlighting it
• If you’re knocked prone while mounted, you must make the same saving throw.: Knocking you prone may unseat you without affecting your mount. You'll land somewhere appropriate to the source of whatever knocked you prone.
• 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.: You don’t get a save in this case; instead, you can burn your reaction to stay standing.

Fun Part: Controlling a Mount

While you’re mounted, you have two options. You can either control the mount or allow it to act independently. Intelligent creatures, such as dragons, act independently.
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.
-PHB pg. 198

The last part of the basic introduces annoyances. There are technically two types of mounts: controlled mounts and independent mounts. For most cases, you would simply use controlled mounts, but for all the Beast Masters, Battle Smiths, Paladins and whoever else there are a separate set of rules for intelligent mounts you can choose to use.

Controlled Mounts

The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.
-PHB pg. 198

Simple. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. I'll run them the same as other creatures that get added along like summons where their turn is concurrent with the owner.

Independent Mounts

An independent mount 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.
-PHB pg. 198

Independent mounts are where things get a bit iffy. Technically they are NPCs, but Find Steed (PHB pg. 240 lists them as unusually intelligent) and Awaken can lead to awkward scenarios where rules don't work together well. Because of this, this set of rules is going to be for NPCs like if you managed to convince a dragon to fly you into combat.

Companions from Class Features and Spells

This is where we dive into new material and apply it to old stuff. Fun fact: Paladin's are the only class that get Find Steed and Find Greater Steed. Therefore, they are essentially optional Class Features, so we're going to lump them into the same category as Primal Companion, Steel Defender and Wildfire Spirit. The Battle Smith Artificer (TCE pg. 19), Circle of Wildfire Druid (TCE pg. 40), and Beast Master Ranger (TCE pg. 61) all have companions as part of their class and share similar restrictions. Will essentially be handing this over to

The only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it to take another action. That action can be one in its stat block or some other action. If you are incapacitated, the spirit can take any action of its choice, not just Dodge.
-TCE pg. 40 - Summon Wildfire Spirit

While the Wildfire Spirit is too small to be a mount except under specific circumstances, they'll all be abiding by the Controlled Mount rules plus having the option for the Controlling Character to use a bonus action to command them to do something else.

But my Mounts are Squishy! How do I keep them alive?

There are some options for this. While most of the class feature pets get built in Armor Class, it may not be enough. Here are some options to help all your pets breathe a little longer

Barding

Barding is armor designed to protect an animal's head, neck, chest, and body. Any type of armor shown on the Armor table in this chapter can be purchased as barding. The cost is four times the equivalent armor made for humanoids, and it weighs twice as much.
-PHB pg. 157

The PHB provided a base cost for barding a horse. That's cool and all for the Horse, but your DM did some math and calculated some extra armor for other sized creatures as well. Large creatures get the PHB treatment for their full body protection. Medium creatures get a 2.5x modifier for their cost and a 1.5x modifier for their weight. Small creatures run the same numbers as Player Characters because of the complexity of their construction.

Armor	Armor Class	Cost (Small)	Cost (Medium)	Cost (Large)	Weight (Small)	Weight (Medium)	Weight (Large)
Leather	11 + Dex Mod	10 gp	25 gp	40 gp	10 lb	15 lb	20 lb
Studded Leather	12 + Dex Mod	45 gp	113 gp	180 gp	13 lb	20 lb	26 lb
Ring Mail	14	30 gp	75 gp	120 gp	45 lb	68 lb	90 lb
Scale Mail	13 + Dex Mod	50 gp	125 gp	200 gp	40 lb	60 lb	80 lb
Chain Mail	16	75 gp	188 gp	300 gp	55 lb	83 lb	110 lb
Splint	17	200 gp	500 gp	800 gp	60 lb	90 lb	120 lb
Plate	18	1500 gp	3750 gp	6000 gp	65 lb	68 lb	130 lb

Dodge!

Dodge is your mount’s default action if they have nothing better to do. It works really well, and if you don’t need to Dash or Disengage there is no reason not to use it. Just remember to bring up that disadvantage to me if I forget.

Mounted Combatant (Feat)

You are a dangerous foe to face while mounted. While you are mounted and aren't incapacitated, you gain the following benefits:

• You have advantage on melee attack rolls against any unmounted creature that is smaller than your mount.
• You can force an attack targeted at your mount to target you instead.
• If your mount is subjected to an effect that allows it to make a Dexterity saving throw to take only half damage, it instead takes no damage if it succeeds on the saving throw, and only half damage if it fails.

-PHB pg. 168

Two-thirds of the feat is devoted strictly to keeping your mount alive. If your mount used Dodge, they get Advantage on Dexterity saving throws and if they pass they can ignore AOEs (that other part of the Dodge action everyone forgets). Isn't that nice?

Pet Addendum:

Creatures that have no mechanical benefits don't need to worry about collateral damage. If you get a pet Tressym that just sorta follows you around, it's basically immortal. The moment you want it to pick up a copper piece at the bottom of the well, it gains one hit point and can die.