No direct train from Dunhuang to Urumqi. You need to take bus from Dunhuang City to Liuyuan, then take train from Liuyuan Railway Station to Urumqi. There is shuttle bus between Liuyuan and downtown Dunhuang, about 2 hours. The train would be in operation during Dec and Jan.
Dunhuang Weather(https://www.travelchinaguide.com/climate/dunhuang.htm) is bitingly cold in winter and is not suitable for traveling. March to October is suitable for visiting.