Satan is frozen in Cocytus, Minos is in charge of examining each soul for judgment, but who is in charge of all of hell?

Satan is indeed in charge of Hell. It's just that Dante presents him as a rather pathetic, impotent figure. Instead of the charismatic, charmingly seductive Satan of Milton's Paradise Lost, we're presented with a hideous but immobile monster, vainly beating his six wings in a futile bid to escape his icy tomb.
There's a sense of anticlimax about Dante's encounter with the Prince of Darkness, and this is intentional on Dante's part. He wants to present Satan as a dumb beast rather than a cunning tempter. He may look pretty fearsome with his monstrous size, three faces, and six huge bat-like wings, but he cannot threaten Dante as he remains firmly trapped in ice.
Satan constantly beats his wings in a desperate bid for freedom. Ironically, though, each time he does so, he simply generates an icy wind that keeps the water beneath him frozen solid. If he didn't struggle, this wouldn't happen, and so he'd be able to make good his escape. But because Satan is so proud, so arrogant, and so full of defiance towards God, he'll continue to keep on trying to fly off, even though it'll leave him trapped in Cocytus for all eternity.