Is this usage possible?

Solution 1:

Wing, in this this sense, is defined as a verb meaning 'throw'. So yes it is possible to use it here.

"The wind threw a thick heap of clouds off westward..."

Although unrelated, the alliteration of "wind" and "winged" can be seen as a great literary device.

In summary, the sentence is both grammatically correct, uses alliteration and features "winged" as a verb meaning "threw".

Solution 2:

Such use of winged is possible, but wafted would be better.

The sense “To throw” of verb wing is less well-known and less commonly used than all but one of its other senses, which are (from wiktionary)

1. (transitive) To injure slightly (as with a gunshot), especially in the arm.
2. (intransitive) To fly.
3. (transitive, of a building) To add a wing (extra part) to.
4. (transitive) To act or speak extemporaneously; to improvise; to wing it.
5. (transitive) To throw

On the other hand, all but one of the senses of waft have proper semantics for use in the question's example:

1. (ergative) To (cause to) float easily or gently through the air.
2. (intransitive) To be moved, or to pass, on a buoyant medium; to float.
3. To give notice to by waving something; to wave the hand to; to beckon.