Do I really need to include a warm up and cool down in my workouts?

Yes!

Why is it important to warm up before and cool down after your workout?

If you’re exercising to maintain or improve your current fitness level, and your workout consists of weight training or cardio, a brisk five-minute walk on a treadmill will serve to prime your muscles with the additional blood flow to be able to handle the work load efficiently. If you head straight into your workout without first warming up, your muscles may not give you peak performance until your body has sufficiently caught up with the additional blood flow your muscles need. 

After your workout, especially a weight training session, another brisk to slow walk on the treadmill for five to ten minutes will help to bring your body systems back to resting rates. While you’re working out, the muscles being worked can receive up to 85% of the oxygen and blood flow your body produces. After you cool down, those resources will return to a more even distribution through all of your organs (your kidneys, liver, stomach, etc.). An active cool down can accommodate this re-distribution more effectively than just stopping and resting right away. It can also help remove built-up lactic acid and reduce muscle soreness.

Where does stretching come into play? You should stretch the muscles you just worked directly after working them to help eliminate the waste produced by the exercise (lactic acid). These stretches should be done before your cool down, because during and after the cool down your muscles lose some of the elasticity they have as a result of the warmth from working them. Stretching for this effect should reach the point of just before discomfort and held for eight to ten seconds. If, however, your goal is to improve range of motion, stretch to the point of mild discomfort and hold the stretch longer (up to a minute). If you perform a stretching regimen as your exercise session, be sure to take extra time to warm up your muscles before you begin.  

It may seem like a good idea to shave ten or fifteen minutes off your workout by skipping the warm up and cool down, but your workout will be more effective and your recovery less painful if you don’t.