Another discussion of this matter is available here:
What makes this one particularly interesting is that the author started in the "pro-wings" camp but ended up in the "anti-wings" camp, and this page supplies his reasoning for it.
The usual "literal vs figurative", analysis of "winged speed", etc serves as an opener, but - IMO - the most compelling part of his argument begins about two-thirds down the page, where he makes an attempt to calculate what the wingspan of a winged Balrog would be (based on the chasm being 50 feet across, a dictionary definition of the word "chasm", the hall being wide enough for two rows of pillars, and a - admittedly flawed because it depends on pre-LotR material - deduction of a Balrog's height).
While it does make for a compelling argument, there are - as I said - flaws in it (the example I gave isn't the only one) and as always we're left with the words of Tolkien himself:
Of this two things are said, though which is true only those Wise could say who now are gone.
It's probably worth chiming in with my own reasoning here. First of all, I'm going to assert that when many people mentally picture the Balrog, they picture something similar to an Ifrit/Efreet from Arabian mythology:
An ifrit is an enormous winged creature of fire, either male or female, who lives underground and frequents ruins.
It's necessary to dispel that image (and I'm going to repeatedly hammer this point home so forgive me if I seem to be overdoing it) because when the Balrog is first encountered it actually has no fire at all:
Something was coming up behind them. What it was could not be seen: it was like a great shadow, in the middle of which was a dark form, of man-shape maybe, yet greater; and a power and terror seemed to be in it and to go before it.
Aside from circumstantial reasoning, such as that Gandalf would have described fire and heat when the Balrog entered the Chamber of Mazarbul, this description makes it unassailable: the Ifrit mental picture is incorrect and the initial encounter with the Balrog is with a being of pure darkness and shadow (picture something like Radagast's encounter with the Necromancer in the first Hobbit movie here).
It's only when the Balrog leaps over the fiery fissure that it then becomes the famously-described creature of "shadow and flame":
It came to the edge of the fire and the light faded as if a cloud had bent over it. Then with a rush it leaped across the fissure. The flames roared up to greet it, and wreathed about it; and a black smoke swirled in the air. Its streaming mane kindled, and blazed behind it.
Even here we see that the shadow element was sufficient to douse much of the light from the fissure, so the Balrog's primary element is definitely shadow - fire is just secondary, and the "Ifrit image" must be discarded. This is also seen in Gandalf's description of after the Balrog fell into the abyss under the Bridge:
His fire was quenched, but now he was a thing of slime, stronger than a strangling snake.
So a Balrog's fire can be put out, further weakening (if it were even necessary to do so by now) the "Ifrit image".
Now for the "wings", and let's look at the first mention:
His enemy halted again, facing him, and the shadow about it reached out like two vast wings.
Again we're not talking about the fire element, we're talking about the shadow, and at this stage the shadow is starting to spread out and take the shape of wings. Now for the next bit, and here I'm going to quote a little extra (emphasised) than is usually done:
The fire in it seemed to die, but the darkness grew. It stepped forward slowly on to the bridge, and suddenly it drew itself up to a great height, and its wings were spread from wall to wall...
Again, Tolkien de-emphasises the fire and strengthens the shadow, and the wings described are clearly those that the shadow "reached out" into the form of (and remember that the shadow, when the Balrog was first described, was not something separate around it, but was described as part of it: "it was like a great shadow").
The evolution of the wings clearly takes the following stages:
- When the Balrog is first encountered there is no description of "wings"; the Balrog is not an Ifrit, it's a creature of shadow and shadow only that subsequently catches fire.
- The shadow form is initially smaller but spreads out like wings at the start of it's encounter with Gandalf: "the shadow about it reached out like two vast wings" - nothing about "fire" here.
- Following Gandalf's challenge, the fire dies down ("the fire in it seemed to die") and the shadow form ("but the darkness grew") has by then become wings which "spread from wall to wall".
What we have here is - as I've said multiple times above - not a fiery winged demon like an Ifrit, but something quite different. Something that may have fire somewhere in it, but is primarily a being of darkness and shadow (see also Valaquenta: "their hearts were of fire, but they were cloaked in darkness"), and that darkness/shadow is mutable. In this encounter the shadow changed to take the form of wings, which seems to be what Tolkien is clearly describing.