Pope does tell us that the Sylphs
As now our own, our Beings were of old,/And once inclos'd in Woman's beauteous Mold;/Thence, by a soft Transition, we repair/From earthly Vehicles to these of Air. . . .
The fact that Sylphs were female sometimes is a surprise to readers because they assume the Sylphs are feminine, and it comes as a surprise that they are male figures. That, of course, does not tell us what they look like but does give us at least a view of their gender.
Later, Pope provides a more concrete idea of what Sylphs look like:
Some to the Sun their Insect-Wings unfold,/Waft on the Breeze, or sink in Clouds of Gold./Transparent Forms, too fine for mortal Sight,/Their fluid Bodies half dissolv'd in Light./Loose to the Wind their airy Garments flew,/Thin glitt'ring Textures of the filmy Dew. . . .
Pope reminds us that Sylphs are invisible to humans because they essentially have no substance, but we know at least that they have wings and wear "airy Garments."
At the end of the passage above, Pope gives us another glimpse of Ariel:
Amid the Circle, on the gilded mast,/Superiour by the Head, was Ariel plac'd:/His Purple Pinions op'ning to the Sun. . . .
The description of Ariel's wings as "Purple Pinions" has a dual purpose: it reminds of his "Sylph" nature, and the fact that some of his feathers are purple, the color of royalty and power, signals his leadership position in the world of Sylphs.
Because Pope's description of Sylph's seems incomplete, I think we are meant to understand that Sylphs are creatures of the air, invisible to us, but have sufficient power to carry out their various tasks in guarding Belinda. Visualizing Ariel, for example, as vaguely fairy-like, with male features, is most likely yields an accurate picture of a Sylph.
There does not appear to be any direct description of how Ariel appears. All we are told is that he is a sylph, as he reveals himself, and that he is a small, winged creature who is able to control an army of similarly tiny sylphs and fairy-like creatures that he can summon up at will to defend Belinda. Note what he says about himself in Canto I:
Of these am I, who thy Protection claim,
A watchful Sprite, and Ariel is my name.
Late, as I rang'd the crystal Wilds of Air,
In the clear Mirror of thy ruling Star
I saw, alas! some dread Event impend,
Ere to the Main this morning's Sun descend,
But Heav'n reveals not what, or how, or where...
What we are told about Ariel in this poem therefore concerns his status, identity and role rather than his physical appearance. The fact that he mentions flying in the "crystal Wilds of Air" obviously indicates he has wings, and his small size is suggested by the way that he has to lay his lips against Belinda's ear and get so close to her. We therefore imagine Ariel to be a fairy-like creature with gossamer wings or something like this.