Catherine & Cloud
Catherine and Cloud are Link's two horses. Catherine was Link's bay stallion in the cartoon/comic series, while Cloud was a mare from the adventure books. I'm not sure what colour she is, possibly grey. NB - In my fanfics his horse is called Carefree; A hearing error on my part, the name has stuck!
Dowser is the court hound, very likely to be either Zelda's or the King's pet. He is quite big amd shaggy in appearance, and usually very friendly to newcomers. Dowser can usually sense the presence of evil - for example he knew that Ganon was pretending to be a Prince from another land, in order to fool Link and Zelda into letting him see the Triforce.
Storm is Zelda's horse in the comics. It looks like a white stallion, could be a mare though. She also had a white horse in the cartoon series too, possibly with the same name.