The phrase "side pony" refers to a specific hairstyle where the person's hair is gathered and tied at the side of their head, instead of at the back. Full definition
For the next style, we pulled my hair into a low side pony tail with those pretty waves flowing over my shoulder. (janastyleblog.com)
Pull all your hair to one side, twist loosely, and secure it about halfway down the «tail to create Vanessa Hudgens's flirty side pony. (seventeen.com)