Winter in Shanghai is milder and shorter than that in Beijing (December to February), with little snow and most of time moist. The temperatures are usually above freezing, while feel colder due to the humidity. This is common in Southern China during winter season.
Do prepare plenty of warm clothing and reserve heated hotel rooms when you travel to Shanghai in winter season. The popular shanghai attractions like the Bund, Nanjing Road, Oriental tower, Zhujiajiao water town are still open to tourists in winter and there are less tourists around; if time permit, extend to nearby Suzhou and Hangzhou and view the typical Chinese gardens or water towns.
The celebrations of Chinese New Year including fireworks displays, lantern parade, or ceremony held in Longhua temple of Shanghai, offers great holiday experience for your shanghai trip.