Missouri weather is pretty bipolar. One day, it can be 89 degrees, and the next it is below freezing. Fall usually brings in some of the best weather Missouri has to offer. It gets a little chilly during the night, but during the day, it's usually in the high 60s or low 70s.
Winters can get bad. During the winter of 2011, Mizzou had a small blizzard that caused campus to shut down for three days. Don't expect that every winter, though; the last time school was shut down was in 2006, and the time before that was in 1998. Winters are also very cold—not just due to the low temperature, but because of the wind. Spring is usually very rainy and overcast, so bring an umbrella. Summers are hot and humid! Humidity is probably the worst weather-related experience in Missouri.