AOE attacks hit everyone in the attack zone as a separate attack.
Mounted Combatant: 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.
IF you and your mount are occupying the same square (such as when you are riding the mount) you also are targeted by the AOE attack. The ability for your mount to receive no damage on a DEX save is meant to keep your mount up and in fighting condition. No where does it state that you yourself receive this benefit as well.
An Air Elemental makes an exceptional mount at any level for most any character. Acquirable via diplomacy, Planar Ally, Planar Binding, or the Air domain granted power (among other methods), Air Elementals have the following features as mounts:
Size:
Air elementals come in sizes ranging from Small to Huge and thus can make excellent mounts for creatures of sizes Tiny to Large. A Large Air Elemental is, unsurprisingly, Large.
Speed:
Air Elementals have a 100 ft. fly speed with maneuverability: perfect. It's not Dragon fast, but it's very, very nice, and Dragons (that aren't mercury dragons, and those are CG) don't fit your maneuverability requirements.
Carrying Capacity:
A Large Air Elemental can carry a little over 1/3rd as much as your warhorse without strength boosts. This enough to pull your carriage as a heavy load (through the air, mind you) if the Warhorse was pulling it as a light load. In any case, you should be fine here with even a minimal investment in strength-boosting gear (or you could also get a bigger Elemental). Worth noting that 4 rounds every 10 minutes, your elemental can Whirlwind to carry whatever fits inside its increased volume at full speed, instead of the normal carrying capacity rules.
Fly speed: Check
Maneuverability: Check
Trainable by someone else: 1) You can Planar ally for these. 2) You can Planar Binding for these. 3) You can Command Air these. etc etc etc. Very much easy to get.
Neutral or Evil alignment: Check
Loyal: You can have them mindslaved for you by a Cleric, and as long as the Cleric's happy you're good. Alternatively, they speak Auran and are vulnerable to Diplomacy. Alternatively you can use Planar Binding to ensure service.
Bonus Features:
- Despite carrying your carriage in a whirlwind, the text of the whirlwind ability indicates that the Elemental has perfect control over the motion of objects it carries and their location upon exiting the whirlwind. Apparently it's a pretty smooth ride.
- +11 initiative score should help with keeping your stuff safe in unexpected combats and such.
- You can talk to it easy enough.
- Can handle itself okay in combat if forced to.
- Is eligible for both the Half-Fiend and Half-Dragon templates, which don't make the creature harder to train or obtain (availability permitting), but do make it more powerful (for example increasing its carrying capacity and adding useful SLAs)
Best Answer
Yes
Player's Handbook, p. 198:
However, there are limitations:
1. The DM has to say yes
It's undefined what is an "appropriate" anatomy, leaving that judgement up to the DM. It doesn't say they have to be a quadruped. Since Luke Skywalker can carry Master Yoda in a backpack, and the baby backpack is a real thing, it seems plausible that a human with a backpack can carry a gnome.
2. You can't control the mount's movement
3. You can be knocked off
4. You count against their carrying capacity
While horses can carry a great deal of cargo, humans have encumbrance limits, standardly 15 times their Strength score, but using the variant encumbrance rules they are encumbered at 5 times their Strength score (PHB p176). Gnomes and halflings tend to weigh 40 to 45 pounds, so an average-strength human may have difficulty carrying you and your equipment and their own equipment.
However, you will be pleased to know that other than encumbrance, there is no penalty to your "mount" for carrying a rider (PHB 198):