The very first animal you step into in Seasons Story: Friends of Mineral Town is a pony. After servicing him for about three full seasons, he will transform into a horse and you can use him to move around town at a much faster pace. If you want to get more pets, you need to unlock Van, the traveling merchant first.
You can only get more pets when an animal you already own has 8 or more hearts in its friendship gauge. To check your pet's friendship level, open the menu and go to the Relationships tab, then choose pets. Here you will be able to see the individual friendship level of any animal you own.
To increase your pet's friendship level, you need to interact with him every day. Telling your pet that you love them and giving them a brush stroke every morning is a great way to develop their friendship level. You can also buy Treats from Van for 1000 gold each, which will increase your friendship level, if you don't want to wait to get a new pet, you can speed up your pet's friendship level from this way.
Being better friends with your pets will also mean that they are better at playing with you. You can buy a ball or a frisbee from Huang, who lives in Zach's beach house, and then you can play fetch with them when they grow up. You can buy the ball for 100 gold and the Frisbee for 5000 gold. You can use the ball to play with them when they are younger, which will also help increase your friendship level with them.
