Briefly, the climate of China varies from the northern to southern areas. Among your destinations, Tibet, Xian and Beijing belong to the northern areas. Around the October to November, it is cold in Xian and Beijing with an average temeprature of about 10-12 C. The lowest temeprature could be about 5 C then. Comapred with Beijing, Xian is a little warmer, but not much. At that time, you need take along over-coats and sweaters.
As for the weather in Lhasa, Tibet, in the early and Mid of Oct. the average temperature is about 13-15 C, while from the late Oct. to Nov. it becomes cooler and cooler, with the average temeprature about 5 C. Sometimes, it may be about -5 C. So you'd better take alonf wool sweaters, leather jackets, wool gloves and other warm clothings if you want to go there then.
Yangtze and Shanghai would be warmer than the ablver three destinbations. The average temperature could be about 15-16 C. It would be a good traveling time except the late November. You need take along long-sleeved warm clothing, thin sweater and coat.