Habitable planets are commonly imagined to be temperate planets like Earth, with areas of open ocean and warm land. In contrast, planets in snowball states, where oceans are entirely ice covered, are believed to be inhospitable. However, we show using a general circulation model that terrestrial planets in the inner habitable zone are able to support large unfrozen areas of land while in a snowball state. Due to their lower albedo, these unfrozen regions reach summer temperatures in excess of 10 \textdegree C. Such conditions permit CO2 weathering, suggesting that continental weathering can provide a mechanism for trapping planets in stable snowball states. The presence of land areas with warm temperatures and liquid surface water motivates a more-nuanced understanding of habitability during these snowball events.