As you exercise, your metabolic rate goes up and you sweat to prevent your body from getting too hot.
According to Dr. Ollie Jay, founder of the Thermal Ergonomics Laboratory at the University of Ottawa, "We don't start dissipating enough heat to balance the elevated metabolic heat production until about 30 or 45 minutes of exercise."
Basically you create more heat than you sweat out during your workout. Afterwards, your body catches up.
Once exercise is completed, your metabolic heat production slows, but your body continues to lose heat, because you may continue to sweat.
Essentially, it's the warm-up in reverse. You're dissipating more than you're producing, and your body may take you one step too far, causing you to become chilly.
After a workout, women tend to lose heat more quickly than men, because their skin's surface-area-to-body-mass ratio is higher.
And although this probably goes without saying, you shouldn't keep wearing your sweaty gym clothes after a workout. If you're walking around in sopping wet training gear, that's a whole other problem.