Ah, I've just realised my mistake. He has a black cloak when leaving Rivendell, but arriving he has a red/brown one.
During the time he travels to Moria and leaving Rivendell, he has that black one. He discards it in Balin's tomb I think, but it's not entirely clear.
When he's blowing his horn at Amon-Hen, that's the cloak gifted to him by Galadriel
That's a green/grey coloured one.
Games Workshop may have not added the cloak because there was a miniature of him produced with a cloak, and gamers could sculpt their own cloak on if they wished.