Unfortunately, there's no way to directly grow your foal in Pony Island. Foals stay as foals throughout the game. They're cute and fun to play with, but they don't grow into adult ponies.
However, if you're looking to grow your character, you can use the growth potion available in the game. This potion will make your character grow taller and stronger.
Remember, Pony Island is about exploring a mysterious island, solving puzzles, and having fun with your pony friends!