Sweating doesn't make you burn any extra body fat. Sweating is how your body regulates internal temperature, as the sweat evaporates cooling you down through 'evaporative cooling'. Actually, in theory, being cold would make you burn more calories than being hot and sweating because unlike sweating to cool down, to raise internal body temperature the body must burn fuels such as Carbohydrates or fat. That being said, neither sweating or freezing is going to help you lose weight. Diet and exercise, my friend.
As someone else already pointed out, sweating is often used in the short-term (ie. a day or a couple of days) by pro-athletes to meet weight restrictions, but the only weight being lost is water, which weighs exactly 1.02789 grams per cubic centimeter. You regain that weight as soon as you regain lost moisture.