Your friend is perhaps referring to Daniel 7:7:
After this I saw in the night visions, and behold a fourth beast, dreadful and terrible, and strong exceedingly; and it had great iron teeth: it devoured and brake in pieces, and stamped the residue with the feet of it: and it was diverse from all the beasts that were before it; and it had ten horns.
Note that this was "a vision", not reality.
And a few verses later, Daniel 7:24 explains what the symbolic horns meant:
And the ten horns out of this kingdom are ten kings ...
Similarly, Revelation 13:11 says:
And I beheld another beast coming up out of the earth; and he had two horns like a lamb, and he spake as a dragon.
But Revelation is a symbolic vision, not to be taken literally.
Horns are used to represent power, as in Revelation 17:12, which explains:
And the ten horns which thou sawest are ten kings ...
(Don't accept individual verses out of context. Let scripture interpret itself.)
As for depictions of Satan (and his demons), 2 Corinthians 11:14-15 says:
And no marvel; for Satan himself is transformed into an angel of light. Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness ...
As an angel, Satan can appear as whatever he wants.
It's obviously to his advantage for him and his ministers to appear as attractive, charismatic, trustworthy, righteous people.
His portrayal with horns etc. is symbolic, and intended to scare us away from him.
On the other hand, some suggest that this false depiction might actually be a tool of the devil himself.
In "The Screwtape Letters", C. S. Lewis's demonic character offers a suggestion to another demon:
The fact that ‘devils’ are predominately comic figures in the modern imagination will help you. If any faint suspicion of your existence begins to arise in his mind, suggest to him a picture of something in red tights, and persuade him that since he cannot believe in that (it is an old textbook method of confusing them) he therefore cannot believe in you.
Earlier, in 1864, Charles Baudelaire, in "The Generous Gambler" stated:
The loveliest trick of the Devil is to persuade you that he does not exist!