So we know that earth ponies have strength and a mystical connection to the earth, pegasi have flight and weather control, and unicorns are mages.

Assuming thestrals are also magical in some respect, what kind of innate racial magic do you think they would have?

My suggestions are:

• Can magically quieten their hooves and move stealthily even when it shouldn't be possible.
• Can walk on ceilings and walls, and even spider climb, possibly as a variation of pegasus cloudwalking? (I know changelings can also do this, but I assume it's more due to secretions from their legs rather than magic).
• Have a sort of higher than normal 'hunting instinct', even by predator standards, and can track down their targets to the most well hidden hiding places with ridiculous accuracy. In some cases, even arriving at a rendezvous point before the target.

I have one.
Strength and speed higher than a pegasus but around or more than a normal earth pony.
And lets throw night vision in there too.
Plus all their senses are enhanced greatly compared to normal ponies.

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From a biological standpoint, feathered wings on a bird have long distance flight capabilities, whereas membranous wings like on a bat are great for maneuverability. Thestrals would be good combatants while sharing most of the same abilities as pegasi.

I try hard to differentiate them from pegasi in my stories. I don't want them to be just upgraded pegasi but instead their own distinct thing.

1. Greater hunting instincts.

2. Lack the ability to cloudwalk.

3. Weather manipulation is on a much smaller scale. They can manipulate small amounts of fog or smoke in terms of shape, but can't really manipulate weather patterns in any way shape or form.

4. While they lack cloudwalking they can move quickly through tree branches, caves, and underbrush without causing branches to shake, leaves to rustle, or small rocks/gravel to fall.

5. Worse at high altitude flying or long distance flying far better at low altitude flying or flying in confined spaces. Accelerate faster in the air but reach lower top speeds so better for quick bursts of speed but worse for long distance travel.

6. Better natural night vision.

7. Wings are more agile as appendages. Can get a better grip on something with a wing than a pegasus could.

8. More vulnerable to the cold than a pegasus as their wings are less insulated.

I've always taken the idea similar to the quiet hooves but grander. My headcanon is that the can become invisible OR travel in shadow it's honestly a toss-up but that is why the 'legend' of never seeing a Thestral unless death is near is a thing still generally in my stories I try and write.
And yes perfect night vision with a slight sensitivity to light it's not crippling.

6393047 Oh, you can tweak the reader with any number of red herrings in a story with our favorite BatMares, but remember balance.

(+) Greater night vision (-) Nearly blinded in full sunlight
(+) Prowls the night (-) Sleeps during the day (Remember, there's overlap here, so ponies of both types are active in the morning and evening hours)
(+) Stealthy (-) Viewed as a little creepy by other ponies.
(+) Sexy (-) Although mostly among their own types, or it goes "Hey, wake up. Come on. It's not even midnight yet, and I want to play."
(+) Better flight in the rain, gliding, diving (-) less maneuverable when dry, accelerating or climbing

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My idea is that they are the miners of Equestria. That their eyes and ears are better suited to area with little to no light and that their magic helps grow minerals as well as ore. It's why Equestria has so many gems poping out of the ground

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Might as well throw in my own 2 euro cents

Of all the pony tribes thestrals are considered to be the most enigmatic. Though many consider them to be an offshoot of the pegasi, their inherent abilities and close ties to magic are way too different for something as simple as a stable mutation. Many argue that thestrals have more in common with unicorns since place in the world is just as weird. After all, earth ponies and pegasi represent reasonable things, like earth and skies, whereas unicorns and thestrals represent such abstract concepts like stars and darkness.

Despite the various theories, all three tribes agree on one thing: thestrals are strange. This lack of knowledge comes from the fact that few, if any thestrals, have bothered to integrate into the pony society. Then again, considering how much thestrals have been persecuted throughout history, one can hardly blame them.

One of the big reasons why thestrals have been shunned is due to the fact that they drink blood. That by itself wouldn't be much of a problem, there's plenty of cows and pigs in Equestria. It's because plenty of thestrals have sunk their fangs into pony necks that there is a reason for concern. Most thestrals limit themselves to non-pony blood or, if it's completely unavoidable, do their best to take only a very small amount, but it is a temptation that is hard to resist and not every thestral has a strong enough willpower.

In many ways thestrals are well suited to sate their thirst for blood. Their innate abilities make them excellent predators. Excellent eyesight and hearing makes it easy for them to locate their prey. Though it should be pointed out that their eyes are very sensitive to light, which is why they prefer to go out at night, though it is not the main reason for their nocturnal nature. Night is when their more magical abilities come to life.

Thestrals in general have an interesting ability to blend into the background. Unless the pony is focusing their willpower and looking directly at the thestral, it won't take long for the pony to forget about the thestral's presence, even though the thestral is standing right next to them. At night, it is impossible to see or hear a thestral in the shadows. Not unless they want to be seen. Torches, candles or other artificial sources of light can be used to counter it, but should they go out...

Moonlight might provide a way for a pony to spot a thestral, but it would also expose them to the full power of thestral's abilities. Thestrals generally are said to have the ability to confuse ponies with a mere eye contact, but if either one of them is standing in the moonlight, it is fully possible for the thestral to mesmerize its victim. Depending on the willpower of the pony or how long ago the thestral drank blood, it can range from temporary disorientation to a near total control over the pony's mind. It doesn't last long, but sometimes it is more than enough.

One interesting note on thestrals and moonlight is the belief that if you cast a shadow in the moonlight and a thestral stands on it, your shadow and by extension, you, will be pinned to the ground. An interesting tale, but surely it is only an old mare's tale.

What about the ability to the shadows around then to their will, to be more stealthy.

I meant to control the shadows around themselves.

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I'm not sure about the vampirism, but I like the idea of blending in, even in broad daylight.

I always saw them as having enhanced senses, as well as better turning in the air and wall/celling hanging/walking, along with being able to walk on clouds but not move or manipulate them like pegasi can

Being as oblivious as Fnar the unborn is a given power. How about different fruits giving them different powers like in the Bunnicula knock off?

Arctophillia, Since their entire species are essentially teddy bears; why not just give them the standard weakness package such characters have against people that use blame, entrapment, emotional blackmail, compulsions, curses, seals, geas, psychological traps, fear, obligation, guilt, or logical binds?

The Othello effect, far from being a weakness, will become the ability to shatter any illusion, delusion, miracle, magic, or similar if they don't give into their natural predatory (or hare brained Norman Gates) instincts and become a Goon? For instance, becoming something like the "Nimona" character but less in the changeling sense and more like imprinting on a baddie or anarchist who is less evil than the reigning hegemony and battling one's inner demons.

Or, you know being a homogenous species more skittish than Fluttershy to everything else sapient, simultaniously perceived as stupid or dumber than Winonna, and then revealing they have all the powers of a Mimikyu or Necromancer like Ainz Ooal Gown.

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Those fangs are there for a reason.
In my headcanon thestrals are something between vampires and faeries. Even without the blood sucking thing, their habits make ponies nervous. If not for Luna, they would have been hunted to extinction. Granted, Luna's banishment lead to a very dark chapter in thestral history until Celestia stepped in. However, it wasn't until Luna's return that active attempts to integrate thestrals into pony society began. There is still mistrust on both sides, but things are slowly getting better.

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Assuming thestrals are also magical in some respect, what kind of innate racial magic do you think they would have?

Well, horses are notoriously sensitive, enough so that they can feel flies on their fur. Bats are known for their echolocation, but only the insectivorous ones. If we're assuming bat ponies (never using the Harry Potter term, sorry) are closer to the Rousettus genus, then they'd have a mix of micro-and megabat traits.

So, if we apply this logic and rule out what the other tribes have, we're left with heightened senses, as suggested before, and an echolocation ability similar to that of Daredevil. You can go the extra mile and make them have innate kung fu skills, particularly the ability to stick to an opponent and move along with them (see also: The Landlord from Kung Fu Hustle) or give them a parallel to pegasus wings becoming sharp blades, by making the bat wings be like a shield of steel (see also: Batfink).

As for what functions this might give them, the actual points you might want to use in a story, diagnostics of varying degrees would come natural to them. They can feel someone's fever, hear a heart skip a beat, notice a foal's stomach churn with nerves... basically, they would be the kind of ponies who aren't as oblivious as the rest of them. They'd be the first to notice things are going wrong, be it in medicine, diplomacy, or education.

Another point that's worth noting is that alicorns are supposed to encompass traits from all tribes. So what do Celestia, Luna, Cadence, and Flurry do that we would consider not natural to the other tribes?