The stereotypical situation of a snowball picking up both mass and speed as it rolls without slipping down a hill provides an opportunity to explore the general form of both translational and rotational versions of Newton's second law through multivariable differential equations. With a few reasonable assumptions, it can be shown that the snowball reaches a terminal acceleration. While the model may not be completely physically accurate, the exercise and the resulting equation are useful and accessible to students in a second year physics course, arguably.