I can't remember how this happened in the books, but in the Half-Blood Prince film's train scene, Draco's actions seem to make it very clear that he knew that Harry has an invisibility cloak. When did he learn of this?
He was surprised to see Harry's disembodied head floating around in Harry Potter and the Prisoner of Azkaban. If he's got half a brain, he almost certainly worked out later that Harry was using an invisibility cloak, although there are other spells and charms that could achieve much the same effect.
Crabbe stumbled – and his huge, flat foot caught the hem of Harry’s Cloak. Harry felt a great tug, then the Cloak slid off his face.
For a split second, Malfoy stared at him.
‘AAARGH!’ he yelled, pointing at Harry’s head. Then he turned tail and ran, at breakneck speed, back down the hill, Crabbe and Goyle behind him.
Harry tugged the Cloak up again, but the damage was done.
We don't get proof positive until a couple of books later, in Harry Potter and the Half-Blood Prince.
Without warning, Malfoy pointed his wand at Harry, who was instantly paralysed. As though in slow motion, he toppled out of the luggage rack and fell, with an agonising, floor-shaking crash, at Malfoy’s feet, the Invisibility Cloak trapped beneath him, his whole body revealed with his legs still curled absurdly into the cramped kneeling position. He couldn’t move a muscle; he could only gaze up at Malfoy, who smiled broadly.