The coldest period is from the end of January to early February - usually during the Chinese Spring Festival(https://www.travelchinaguide.com/essential/holidays/spring-festival.htm) . The awfully coldness usually lasts for only several days and it may snow. The temperature is not as low as some cities in north China like Beijing, but the humid cold wind is a torture for even the northerners. Sweater and overcoat are necessary in winter. It is Ok to visit Shanghai during that time and you can experience the Chinese troditional festivals there, but you need to prepare well for the cold weather. Usually, Spring and Autumn are the best time to travel to Shanghai.