Warming down or Cool down?

Hello to all,
There is one question that has been bugging me concerning the purpose of warming down. I can understand that we warm up so that the ligaments become more stretchable (feel free to correct me if I am wrong). But, I have never heard of any kind of sport etc that when someone finishes it then he warms down, he almost always puts on some ice or some special cream if he thinks he might be injured.
So why it is so different here in PE?

Thanks in advance.