Many will recommend you to visit north but I'd highly recommend you to visit Jaisalmer or Kutch. the place gets crazy during winters with extreme temperatures, crazy star gazing and bon fire with traditional food and dance with locals!!! P.S. am not sure about the desert festival but if you are going do check if some be during trip it will be the best thing!! Happy Traveling!!
Since it's winter , You can prefer for Manali, Simla, Leh in the north. Rann of Kutch for witnessing a full moon day. Down south u can opt for Coorg in Karnataka ,Ooty, Kodaikanal in Tamil Nadu , Kollam, Varakala in Kerala.