The Gemara in Rosh Hashana 24b and Avoda Zara 43b learns out from the pasuk לא תעשון אתי that we are not allowed to make representations of many things including מלאכים. This halacha is brought down in Shulchan Aruch in יו"ד סימן קמ"א. Since there is an issur to create a representation of a מלאך we need to know what it looks like so we know what not to do. Interestingly enough none of the commentaries on the Shulchan Aruch on the page explain what a מלאך looks like. However, the Ran in Avoda Zara comments that a representation of a מלאך is a human being with wings because this is how a מלאך is perceived by a נביא.
It comes out that this Ran would seem to be the source for the depictions of מלאכים with wings.
I addressed this gemara in a different context relating to a 7 branched menora in a previous post A 7 branch Menora
