The Horse and Dog
The two pets you can receive in the game are a horse and a dog. They will both live inside the Pet Barn, which is just west of your house. Inside the Pet Barn will be 2 food troughs. You will have to put Pet Food in the food bins every day, even if you leave the horse and dog outside. The Pet Food can be purchased from Mirabelle's shop for 10 G each and there is no way to manufacture it on your farm.When you first start out you won't have either pet. You will need to increase your friendships with other villagers before you will be rewarded with animal companions.
The Horse
You can ride your horse around the island and outside of your farm. To mount your pony, stand next to it and tap on its back. To dismount you just have to tap on your charcter. You can ride the horse in and out of the Pet Barn.
If you leave your horse in an out-of-farm area overnight, it will return to your farm the next morning. The horse will be running around your farm land and you'll have to catch it if you want to ride on it again. The horse likes to run and doesn't stay in any particular spot for very long.
The horse festival is on Summer 23. The more hearts your horse has, the better it will fair in the judging. You will win if you have at least 7 hearts.
The Dog
If you leave your dog outside, and it has a lot of hearts, it will scare away the wild dogs that randomly appear on your farm. The wild dog's goal is to scare your livestock and poultry by startling them with its fierce bark, so having a dog of your own will even out the battlefield.