Ongoing climate changes reportedly affect the potential distribution and carbon sequestration potential (CSP) of forest vegetation. The combined effects of increasing temperature and decreasing precipitation on these features of forest vegetation are poorly understood. In this study, classification and regression tree (CART) models were used to predict the potential distribution and estimate the CSP of forest vegetation in Yunnan Province, Southwest China, under different simulation scenarios. The minimum temperature of the coldest month (TMW) was the main factor limiting the suitable habitat of all forest vegetation types except for warm–temperate coniferous (WTC) forests. When the temperature increased by 1 °C and the precipitation decreased by 20%, the potential distribution area of the 7 forest vegetation types decreased by 12.41% overall. The potential distribution of WTC forests was the least sensitive to temperature increases and precipitation decreases. The CSP of vegetation was higher (1187.69 TgC) under the constant temperature and 10% precipitation decrease scenario than the CSP of vegetation under the 2 °C temperature increase and constant precipitation scenario (647.24 TgC). Specifically, the highest CSP (1337.88 TgC) was observed under the 1 °C temperature increase and 10% precipitation decrease scenario, and the lowest (617.91 TgC) occurred under the constant temperature and 20% precipitation decrease scenario. In summary, the forest vegetation in Yunnan Province has a high CSP under climate change, and the combined effect of increased temperature and decreased precipitation can increase the CSP of forest vegetation in Yunnan Province. This finding is important for improving scientific decision-making and policy planning.