Why would a snowball speed up if it's going down a hill?

A snowball on top of the hill would gain speed as it rolls down because of the relationship between kinetic energy and potential energy. In a given system, the sum of these two, the total energy, remains the same. This is because of the Law of Conservation of Energy. It is the interconversion between these two that causes the snowball to accelerate as it goes downhill.

Kinetic energy is energy in motion. It is related to the object's velocity and mass. Meanwhile, potential energy is energy at rest, and is a relationship between an object and a reference point. For example, a compressed spring has a lot of potential energy as it is compressed 'away' from its resting position (the same is true when it is stretched). This potential energy can be used to do work as the spring is released and goes back to its resting state. In the snowball's case, it starts from the top of the hill and has potential energy due to its elevation. Objects at a higher position have higher potential energy due to gravity. Gravity is pulling them down. 

As the snowball is released and starts going downhill, the elevation decreases and potential energy decreases. Potential energy is at its lowest when the snowball reaches the ground and stops rolling. Meanwhile, as the snowball goes down and its potential energy decreases, kinetic energy increases due to the Law of Conservation of Energy. Since kinetic energy increases, the velocity of the snowball also increases as the snowball rolls down the hill.