When you have a cold and you workout to where you're sweating a lot during that cold then the sweating can help ease congestion during the cold virus.
So exercising is good for you when you have a cold and may make you feel better and at least get rid of the congestion but actually sweating out the cold virus is not possible.
So you cannot sweat out a cold by exercising or doing anything else since the cold virus is inside your body and can only be killed off by medications and your immune system fighting those infections.
Stay hydrated and get plenty of Vitamin C and rest and within a week or 10 days the cold should be over and you should be feeling much better.
Use a humidifier in your room and/or take a hot steamy shower to help with congestion as well.