Per the wiki (and, to avoid spoilers, this article will mostly be riffs on that, so go read it and you needn’t come back unless you want to), it’s a ghostly or supernatural group of huntsmen passing in wild pursuit. It’s made of either elves or fairies or the dead; the leader is often a named figure associated with Woden, but also various kings, symbols of death, bibliccal figures, or an unidentified soul.
Seeing the hunt is thought to presage catastrophe, from individual death to four-horsemen territory, plus abduction into the underworld or fairy kingdom; people’s spirits could be pulled away during their sleep to join the cavalcade.
There is of course a Welsh association with the Cwn Annwn, which is where I come in; from Lloyd Alexander’s Chronicles of Prydain, I’ve got this association of Arawn (Lord of Annwn, more or less the arch-lich) as the vilest undead-typed evil, but these hounds aren’t skull beasts. They’re D&D’s yeth hounds; spooky and supernatural, but otherwise fleshy. Of course, ghosts work that way in myths an awful lot; transparency and incorporeality are traits ghosts may have, but not strictly necessary. Susan Cooper’s The Dark is Rising got me, too; the hunt as choosing a quarry to harry to the ends of the earth has always been a note of mine. Too, the wild calling, fearsome and compelling.
The components of the hunt are variously monstrous; yeth hounds, black giants, riding-goats, giant birds, curses, fire, and calamity; at the head, death itself, or Odin, or Satan, or King Arthur. I think that’s some of the confusion between the land of the dead and the land of the fey; they’re sort of a parallel construction in most myths; the dead dwell with the gods, after all.
What this means is that for D&D-ables, we don’t have THE wild hunt — we have, at best, A wild hunt. It could be fiendish or undead, led by horrors, just like those monks recorded. It could be staffed by valkyries and Odin, leading the dead to their rightful rest (or, of course, manufacturing some dead). Giants. Fey. Heroes from their barrows. Sleepwalkers. Nightmares.
The Wild Hunt of Hell is all ready to go. Hellhounds and nightmares, obviously. It’s a little less clear who the humanoid participants would be. I usually populate hell with the “dead and damned”, so wights and zombies, led by a wraith or bone devil or similar — all the way up to pit fiend if you’ve been naughty. We could use some of the linear-increase souped up creatures from the DMsGuild D&D 5e Monster Expansion, like the wight king or the dread wraith. Or get a few more proper fiendish members; maybe tiefling scouts or thugs or veterans; maybe the cambion; maybe DMsGuild The Codex Malevolence II Fearsome Fiends I (whew, say that five times fast), the yeth hound, the baron cambion. Or the DMsGuild Planar Bestiary, the cavalry devil, the legion devil, their version of a yeth hound.
Because of how myths work, the quarry of this gang is a little unclear. I think it’s basically supposed to be sinners (this is how the devil drags you down to hell), but that doesn’t work for this roster in D&D. They’re out for blood, and if this hunt comes-a-calling, just from sheer bulk of monster we’re looking at trouble. It could be a purely reclamatory force, here to find some unlicensed planewalking. It could be here to drag some errant warlock away. But honestly, regardless of stated intent they’re going to watch the world burn, with that firepower.
Getting caught up in this hunt gets you dead. Getting dead in the path of the hunt gets you dragged to Hell. Which gets you zombied or wighted. Welcome to the hunt. They open up the graves and arm the conscripts. I suspect one could ride with them at extreme risks to one’s soul.
The Wild Hunt of Odin is a less undeady matter. We don’t have a great and obvious Valkyrie yet (oh, there’s something of that name in Kobold Press’ Tome of Beasts, but it feels off to me at the table: I don’t want them legendary, I don’t want them crafting in combat, etc). We can use erinyes for them in part, swapping poison to psychic. But there’s an oddly off-label use I think works even better: we could just use deva stats straight. The Valkyrie as choosers of the slain in this reading are quite literal about what they’re doing, stealing bodies off the field and marching them away with none of this soul business. What heads this chooser-of-the-slain committee? The One-Eyed God hisself seems a bit out of our reach here, but we could put a hero at the head of our army, our Arthur or our Gwydion or whatever. I guess we could say a celestial-typed legendary-kitted-out knight or archmage with double hit points and +4 to everything, but I’m not really thrilled with it without more thought. In any case, then follow our knights and nobles and guards on phantom steeds for the riders and foot; for hounds, dire wolves or, oddly not as far off theme as you’d think, manticores. They’re only challenge 3, their flight lets them keep up, and their fearsome aspect is a good match for what we need here. Just think of the howls! Here’s where we get birds-as-soldiers, too — swarms of ravens, giant eagles, maybe aarakocra as rook-soldiers.
The choosers of the slain are here on a mission, and probably a pretty well known one: create a war, stop a war, make sure the right side wins a war, that sort of thing. They don’t set everything on fire with their passing, and their deva/archmage/phantom steeds give them quite a bit of mobility. Famously, the wild hunt targets wood-fey; this might be the one that does, preparing the way for humanity. They also get to be the cull that removes the undead; maybe they drive out an undead scourge. A service rendered to them will probably be blessed, but with something ambiguous; standing in their way probably gets you forcibly inducted.
There’s quite a few ways into this revel: deva-typed Valkyries pick you up and dust you off, give you a mount and away you go! Alternatively, maybe the master of the hunt turns you into one of the beasts — it’s a thing that happens. In either case, serving in the same interest as the hunt probably leaves you unharmed (or at least cleanly dead), while hindering it leaves you in bad shape. Laying prone in the middle of the road is the safest place to be, for their steeds’ legs don’t reach that low.
The Wild Hunt of the Fey is old and, well, wild. While my Seelie/Unseelie split calls itself Illyrian/Fomori, and my Illyrians are the green, wild, and woodsy fey, the wild hunt is somehow… wilder. It’s the raw stuff, the wild magic. I see this one as the call of the bacchanal, and the thing that makes fey creatures behave madly and in modes older than man. The hunt itself is made of the fey and fey-adjacent creatures. For instance, the elves, the gnomes, giant animals, the blink dogs for they could be called cu sidhe, and the displacer beast hellcats which might as well be cait sidhe). We know there are giants with striking eyes; perhaps use the Fomorian giant here. The leader is probably a drow priestess or drow mage, maybe a (read as fey) djinn since we don’t have ghaele stats — or do, if you check out the DMsGuild Planar Bestiary!
This wild hunt serves at the whim of its master; in general, I assume it’s some old elven grudge. Don’t be someone who an elf from a thousand years ago would hold a grudge against, I guess!
I see this one as the kidnap-you-away-to-fairyland one, the one that encourages you to join in and, once you do, you are a part of it until the hunt ends. Elves should be more vulnerable to it than most, but are resistant to charm, so it’s probably a fear effect. So there’s some spells or magic that they use.
So: At least three wild hunts.