that's your body's response to change in climate. when winter starts, your body is still adapted to the warm and slightly more humid climate of summer/fall. since it doesn't get what it's expecting, it needs to adapt to the change in climate, which takes time. during that change, numerous change undergo in your body, especially in your blood - change in concentration of salts, certain proteins, and blood cells. and those changes are manifested as minor illnesses like cold, cough, mild fever, etc. syrups and antibiotics might help some people and might not work on some. all you gotta do is stay warm, drink warm water for few days and good food - soups like daal, vegetables, and fruits. 
happens to me too, i just eat good food and increase sleep hours until everything gets back to normal, takes about 2-4 days for me. 
if things start getting intense, taking 1-2 pills containing 500mg paracetamol for 1-2 nights before sleep does the job.