A warm basketball is bouncier than a cold one because the molecules in the warm ball hit its inside surface at a higher speed.
As the temperature increases, gas molecules expand with increasing energy and they bounce around faster inside the ball. That's why higher pressure leads to a higher bounce of the ball.
Likewise, a lower temperature will lead to lower pressure. As the temperature decreases, gas molecules contract and move around more slowly with less energy. Thus, lower pressure leads to a lower bounce of the ball.
That's why a fully-inflated ball might appear deflated if the temperature drops dramatically. As you probably already know, that partially-deflated ball won't bounce nearly as high as it would if it were warmer.
Professional athletes and sports teams take temperature into consideration when playing games. They understand that balls act differently in colder weather than they do in warmer weather. For example, football teams playing in extremely cold weather often have to compensate for the fact that footballs will bounce differently, especially when kicked.