Because the virus is more stable and stays airborne longer when it's cold. Cells infected with flu virus are coated in a fatty material that hardens and protects them in low temperatures. (When you inhale a flu particle, that coating melts in the respiratory tract, releasing the virus.) Viruses also stay in the air more easily when the air is cold and dry. When it's humid, by contrast, flu-carrying vapor droplets get heavier and fall to the ground.
Temperature makes a huge difference in transmission rates. In a study published in 2007, flu researchers exposed guinea pigs to a virus at various temperatures. They found that transmission levels were high at 41 degrees Fahrenheit but declined at increased temperatures. At 86 degrees, the virus did not transmit at all. (Slate's Andy Bowers tackled this question for NPR in 2003.)