After exercising, why “cool down” by doing light walking, etc.? Why not just stop. 
If you just stop after a heavy cardio work-out, your heart-rate and breathing will still be elevated, and you’ll be busy pumping all that extra oxygen to your muscles, which no longer need it. Thus you should slow down gradually. I have heard that the extra oxygen can be detrimental, but I don’t know if it’s true.
Becuase if you swallow a match, you might spontaneously combust! 
Sorry, I couldn’t resist.
Zev Steinhardt
There are several reasons for cooling down. If you were running or using your legs, your blood increased there and you don’t want to stop suddenly with the blood pooled in your legs. By cooling down, your body will slowly return to normal circulation instead of abruptly trying to the resting state. Also, you had increased your heart rate and you should give your heart a chance to return to normal slowly, instead of precipitously. Sudden abrupt changes are not good for your body. The converse (obverse, whatever) is true for warming up.
You may have noted that after finishing a marathon, some runners will lie down, raise their legs, and bicycle their legs. That’s another way to get your blood back to your heart and brain. If you stop suddenly, your brain may not get enough blood for a while, since your heart has slowed down but a lot of blood is still in the legs, and you may faint.