Prior to about 650 million years ago, the Earth's surface is believed to have completely frozen and thawed multiple times, each frozen period lasting for millions of years. The term "Snowball Earth" describes the runaway effect of ice expanding equatorward, with its brightly reflecting surface causing reduced absorption of sunlight, increased cooling, and further ice expansion. We used Global Climates Models to better understand the conditions necessary for other planets to be trapped in a Snowball state. We modeled planets that are Earth-like but with ocean-only surfaces. Our object is to investigate and further define the inner edge of the habitable zone - the theoretical region around a star where liquid water can exist on the surface. Our research has big implications for habitability, as liquid water is required for life to exist as we know it. The obliquity of a planet is also very important, as it controls the relative proportion of sunlight received at each latitude. Even within our own solar system there is a wide range. The Earth is tilted 23 degrees, Uranus 97, and Venus 177. We present results for an ensemble of planets with differing obliquities to demonstrate its effects. Furthermore, we also present results for planets around G-type stars, like our Sun, and M-type stars, also known as red dwarfs. Red dwarfs are by far the most common type of star in the Milky Way Galaxy. It is easier to detect orbiting extrasolar planets around M-stars. M-stars tend to have a relatively high abundance of Earth-sized and smaller planets, which are more likely to be rocky - a necessary condition for habitability. The effect of an M star’s solar spectrum on a planet’s energy balance is significantly different than a G star’s, which changes the location of the habitable zone. Our model study provides exciting new insights into the differing dynamics.