I found this museum online which is dedicated to just the presidential pets. You can actually visit this musuem in person in Maryland if you choose! I thought I'd choose a few more esoteric ones to share here.
Old Whitey, a wartime mount and Also a shortlived canary that they called Johnny Ty who died shortly after they tried to pair him with a mate only to discover it too was a male. Zachary Taylor provided a home on the White House grounds for Old Whitey. There was a serious problem for Whitey, however. Many of the visitors to the White House pulled a hair or two from Whitey’s tail for a souvenir.
Rutherford B. Hayes
Pedigreed Jersey cows, the first Siamese Kitten to reach America, Hector and Nellie, Shepherd dogs, one goat, four canaries, two hunting pups, and one spaniel type dog named Duke. Also four kittens, one Mockingbird, and several Carriage horses.
And here is the text of a story on the Cleveland family's pets:
Chicago Daily Tribune, February 12th, 1894
PETS IN THE WHITE HOUSE GROUNDS: Besides the two babies, Esther and Ruth, there are innumerable pets at the White House. Scattered through the broad demesne belonging to the Chief Magistrate are myriads of hares running wild in the grounds and furnishing rare sport for the foxhounds and dachshounds (sic) belonging to Mrs. Cleveland. In the limpid pools of the rose and orchid houses attached to the conservatories are hundreds of imported fish, the principal being the many-tailed Japanese variety of goldfish and the famous paradise fish from Siam.
Game chickens of the shawineck breed are conspicuous whenever a visit is paid to the stables attached to the White House, and Coachman Willis is justly proud of the success which has attended his efforts in raising these pretty fowls. In quadrupeds there is almost every known specimen at the little pagoda-shaped sentry box on the east side of the mansion, where the White House babies in charge of their nurses can be seen every fair day. Gamboling about toddling Ruth, or hiding under the carriage containing infantile Esther, can be seen a cocker spaniel, beautifully marked in white and brown, or a collie, which, though a new arrival, seems perfectly at home amid his new surroundings. Hector, the well-known black French poodle of Mrs Cleveland, is at Buzzard's Bay for the winter, as a companion for the St. Bernard, famous as a medal winner. A bow-legged, squat-figured Dachshund, with long flapping ears, is a great pet with the occupants of the White House, being a recent importation from Germany. Until a few days ago, a voracious tulip-bulb fiend in the shape of a raccoon could be seen climbing up and down the trees facing the Treasury Department, but he made one foray too much, and the story is that a gardener's spade cut his earthly career short.
Mrs. Cleveland's ponies, a handsome pair of animals, which their mistress usually drives to a low and easy going phaeton, complete the list of pet animals contiguous to the White House, birds being tabooed inside the mansion.
Go and find out more on these and all the pets who have called the White House home.