There is a big difference between mobility and warmup. That is not to say that the two are mutually exclusive, but people often confuse the timing and benefits of each.
A warm up is designed to loosen joints and increase heart rate, body temperature, and blood flow to muscles. It is IMPERATIVE to warmup before working out. It will increase performance and minimize injury.
Mobility work is designed to increase range of motion. This can be accomplished by massaging or stretching muscles. The purpose of mobility work is to ensure bodies can move through range of motion required to complete certain tasks. The mobility required to do the splits is different than the mobility required to overhead squats. Humans are born with a huge amount of mobility and lose it due to lack of use or overly tight muscles. Regular doses of mobility work keep us moving well and injury free.
When you come in to workout, your goal is to warm up. Get your body moving. Get your heart rate up. Get a little bit of a sweat going. That is the best way to prepare for a workout. It’s not going to feel great at first. You’re going to feel tight, and your muscles may ache. But give it a few seconds. Before long, you’ll be ready to go.
After the workout, or while watching tv is the time to work on your mobility. You want to be able to put your hands over your head at any time – not just right before a workout.
Also, make sure that your body is warm before your start smashing around. Too much pressure on cold muscles can be more traumatic than beneficial. To be safe, warm up before stretching, too (this one has been debated recently, but no one can claim that being warm before stretching will hurt you). Bottom line: Warm up before workout and mobilize after or any time you can throughout your day.