Roman Catholic images of Satan often depict him as a horned, muscular, bat-winged man in combat with Michael, whose feast is today (right).
In many ancient religious traditions, horns were associated with the crescent moon and thus with fertility, night, darkness, death, and the underworld. On the devil, they signify his power, his association with death, and destructive sexuality.
The bearded muscular figure is consonant with the view found in many religions that the principle force of evil is powerfully masculine (cf. Matt 12:29).
Wings, which allow creatures to dwell in the air and grant them swiftness, i.e. the ability to be “everywhere in an instant,” signify the spiritual nature of both angels and fallen angels. According to Tertullian, “every spirit is winged.” In later imagery, bat wings serve distinguish demons from angels.
Perhaps indicating a more dualist perspective, the Western image depicts Satan – though defeated – as well-matched to fight Michael. I believe Eastern iconography better represents the truth (left).
While the depiction of Satan in the icon contains some of the same elements – e.g. horns and wings – he is dramatically smaller and no match for his fellow angel Michael. Icons consistently represent demons this way – as tiny black specks, rather like flies (which evokes a name of their master: Beëlzebub). This effectively communicates the ultimate insignificance of evil.
(I've written about some of this before).