I am playing TFW, and my players got caought with the wight at the foot hills of Misty Mountains...and it suddenly stuck me, how will they defeat this dangerous foe?

They did with torches which they had prepared them self with before nightfall (very good call). But is there any other way to fight these ghosts of terror? I could not find any information about this. If you have a magic weapon or with fire is the way to go...

Wights seem to have some similarities to the more powerful Wraiths. As such, somehow immersing a Wight in running water might be effective in destroying its material body--especially if the water source is connected to an Elvish realm such as the Running River to the Woodland Realm (I am also taking in consideration that running water is a traditional bane of vampires, so there is another precedent for its effectiveness against evil undead). Afterwards, scatter the remaining armor and possessions, including those of the Wight's lair if it can be located.

The Wight might be defeated through straight combat, but I don't know if such a defeat would prove permanent unless you destroy the body by fire afterward. Again, if the party can locate the lair, scatter any treasure found there, as Tom Bombadi did in the Barrow-downs.

Wight is just an old English word for "person." A barrow-wight is a person in a barrow, a "barrow-person," or "barrow-man."

The barrow-wights, named this by hobbits, are the corpses of Arnoreans that have been reanimated by evil spirits. They wait for the day that the world ends in coldness and darkness, and meanwhile they envy the living their life force and warmth. The wight in The Lord of the Rings is chanting a spell over the hobbits to make them sleep until this end of the world. Then Tom Bombadil arrives and counters with light and hope. The world will not end as the wight believes.

Tom has a power of enchantment though singing, but player-characters won't have the power of Bombadil. I don't think mere fire will hurt a wight. Even dismembered its limbs continue to move. They can apparently cause mists to rise, cause travelers to sleep, and cause fear. They are probably not physically very powerful. Their barrows are enspelled in some way, perhaps to make it possible for a wight to enter it and possess the corpse.

How do you defeat a barrow-wight without Tom Bombadil around? The only permanent solution would probably be to exorcise the barrow and break its spell, and only someone very powerful can do that, not a player-character. To resist them one needs the sort of courage that Frodo shows in the barrow. But whacking one with a weapon would probably be futile—it's not alive in the first place. It has enough magic to keep a corpse from disintegrating; it can probably withstand physical damage in the same way. It thrives in darkness; sunlight is a much more likely weapon.

So, basically, don't get caught by a barrow-wight. Unless you can get it exorcised, flee into sunlight, or at least escape from its barrow.

Stick 'em with the pointy end!

... If you're asking about in-game ways of dealing with them then I seem to recall that the Wight in TfW can be dealt with through usual combat options - I thought it had endurance and/or armour increased (can't remember which) to factor in their resistance to 'normal' weapons.

A wraith in Tolkien is a wholly different thing. A wraith is a living being who has come under the dominion of the Rings of Power, drawn into the spirit-world and enslaved to Sauron's will. A wraith is still alive and it its original body, although its existence is a never-ending torment. A wraith can be killed, though some like the Nazgul are powerful enough beings that killing them is difficult, and all have little physical being in the physical world to affect with an attack. Only men—including hobbits—are susceptible to becoming wraiths; dwarves proved especially resistant to the Rings of Power, and I don't think dark elves would succumb where dwarves did not. Certainly high elves cannot become wraiths, as they already exist simultaneously in the physical and spirit worlds. If Gollum had used the Ring more, and with greater ambition, he would have eventually become a wraith. He stubbornly resisted the wraith-process, to the point that he stopped wearing the Ring regularly and hid it on his island on the lake under the mountains.

The power of the Nazgul seem to wax when they are surrounded by fear and terror. They have little power in the Shire, where most people are only suspicious of the strange Black Riders. They have less power in daylight, as night enhances their connection from the spirit world to the physical world, and they can see things that are hidden to others. It is when Strider stops singing his song that the darkness closes in around the hobbits; they are reassured by the song, and the Nazgul have to wait until it is over before they have the strength to attack.

The Nazgul do fear fire. I'm not sure the reason—perhaps it is the light, or perhaps fire has more effect on the spirit-world than other things.

Wraiths are certainly more dangerous than barrow-wights: they can wear shapes in the physical world even though their actual being is mostly in the spirit world; they can move; and they are slaves to Sauron.

Stormcrow (as usual) provides a couple of excellent answers. I concur in that Barrow-wights & Ringwraiths should be terrifying & rare creatures. Your players' only sensible solution should be flight

That said, however, if you decide to introduce your heroes to what would otherwise be a TPK, you can give them the fire or water option to escape. The water option is tricky, because while the Nazgûl could not cross the Ford of Bruinen against Elrond & Gandalf, they apparently crossed Anduin & the Gwathló at Tharbad. Tolkien admitted to his son Christopher that the water concept was difficult to maintain.

If you still want a rules option, you can tweak this entry from p. 29 of TfW:

Fighting the Night-Wight
The Night-Wight is hard to hit and harder to find. Clever companions will use burning brands to daunt the creature. Based on its special abilities, the Night-Wight loses one point of Hate at the end of the first round of combat for each companion wielding a torch (Fear of Fire) but still profits from its enhanced power at night (Denizen of the Dark). When reduced to zero Hate, the Night-Wight flies away into the night shrieking in frustration (Craven).

Everything said previously pretty much covers the topic, but (though it dates back to 2007) the amount of time I put in on Barrow-wights still compels me to plug my article in Other Minds issue 1.

It can't be said often enough that no one should be seeking to slay a Barrow-wight, and even if they went into it rashly and risk killing your game with a TPK if you don't let them survive, you don't want to let them come out of it bragging. The wight, or his still-animated body parts, or even his disembodied but still potent naked spirit (mercifully bound to the physical of the barrow) should still get the last laugh.

In addition to the raw forces of elemental nature: fire and running water (and therefore maybe frost and lightning), the best bet is partial injury to debilitate the wight sufficiently that he can no longer stop you from getting away.
I don't know whether every blow struck against a Barrow-wight shatters the weapon that delivers it, like it did Frodo's sword, but it's possible. Or maybe only the blows that actually cut through the wight's body parts wreak that entropic revenge. (But don't use the mood-breaker word "entropy" in-game!) But it's those amputating blows are what you want -- set up in TOR terms either as a situation-specific Called Shot option, or simply as the result of a successful Wound (no amount of which, however, will actually kill it!). And then run.

Separating him from his hoard, that being his power source (though it's a difficult Lore test to know this), could severely stunt his ability to regain Hate points to come after you again.
But if you think you've beaten him and got the loot, it's time to make the (arbitrarily!) even harder Lore test to know that keeping the gold is going to bring down the mother of all Mummy's curses on you!

Cheers!
--Os.