From Tar Valon Library
Cloud was a tall gray horse with a black mane and tail that belonged to Jon Thane until Lan bought it for the ride out of the Two Rivers. It was the only riderless horse left when Rand mounted, so he was the one to take him. Rand thinks that Mat and Perrin probably avoided Cloud because though he was very fast, he was not an easy ride and that Lan must have paid a lot to convince Master Thane to part with him (TEotW, Ch. 10).
Rand rides him all the way to Shadar Logoth but is forced to abandon him to get onto the Spray when Trollocs get close and the horses bolt (TEotW, Ch. 20).